MEMORANDUM FINDINGS OF FACT AND OPINION
DAWSON, Judge: This case was assigned to and heard by Special Trial Judge Fred S. Gilbert, Jr., pursuant to the provisions of section 7456(c) of the Internal Revenue Code2 and Rules 180 and181, Tax Court Rules of Practice and Procedure. 3 The Court agrees with and adopts his opinion which is set forth below.
OPINION OF THE SPECIAL TRIAL JUDGE
GILBERT, Special Trial Judge: Respondent determined the following income tax deficiencies and additions to tax:
| Docket No. | Petitioners | Year |
| 814-78 | Sandra L. Powers (Belcher) | 1974 |
| 815-78 | Fred N. Belcher | 1974 |
| 816-78 | Fred N. Belcher and | 1975 |
| Sandra L. Belcher | ||
| 1004-78 | Robert E. Johnson and | 1974 |
| Soccorro E. Vidro Johnson | 1975 | |
| 1015-78 | Osvaldo Montano | 1974 |
| 1975 | ||
| 1177-78 | Martine M. Michell | 1974 |
| 1975 | ||
| 1273-78 | Antonio M. Nieto | 1974 |
| 1975 | ||
| 1306-78 | Joseph Costa | 1974 |
| 1975 | ||
| 1307-78 | Mary F. Woods | 1974 |
| 1975 | ||
| 1308-78 | Sharron I. Sheffield | 1974 |
| 1975 | ||
| 1318-78 | Evelio P. Fraginals | 1974 |
| 1975 | ||
| 1319-78 | Dottie M. Dunlap | 1974 |
| 1975 | ||
| 1407-78 | Lonnie Limon and | 1974 |
| Zenaida Limon | 1975 | |
| 1408-78 | Alejandro Villalvazo and | 1974 |
| Guadalupe Villalvazo | 1975 | |
| 1421-78 | Salvatore Giuliano and | 1974 |
| June L. Giuliano | 1975 | |
| 1422-78 | Pierre Roger and | 1974 |
| Rita R. Roger | 1975 | |
| 1480-78 | Albert G. and Rosalie Lucero | 1975 |
| 2649-78 | Hadji M. Kadmiri and | 1974 |
| Judith I. Kadmiri | 1975 | |
| 3502-78 | Chester R. Whiddon and | 1974 |
| Betty B. Whiddon | 1975 | |
| 4897-78 | Robert Sanger | 1974 |
| 1975 | ||
| 5019-78 | James K. Longworth and | 1974 |
| Mary Ann 4 Longworth | 1975 | |
| 5133-78 | Miguel A. Diaz and | 1974 |
| FeliciaN. Diaz | 1975 | |
| 5225-78 | Charles H. Reid | 1974 |
| 5226-78 | Charles H. Reid and | 1975 |
| Vikki D. Reid | ||
| 2069-79 | Bernardo Sanchez | 1974 |
| 1975 | ||
| 2070-79 | Mary Ann Kelley | 1974 |
| 1975 | ||
| 3715-79 | Osvaldo Montano | 1976 |
| Income Tax | Addition to Tax | |
| Docket No. | Deficiency | (Sec.6653(a)) |
| 814-78 | $ 1,312.34 | $ 65.62 |
| 815-78 | 1,809.40 | 90.47 |
| 816-78 | 4,834.60 | 241.73 |
| 1004-78 | 1,428.44 | 71.42 |
| 1,530.88 | 76.54 | |
| 1015-78 | 2,005.41 | 100.27 |
| 2,389.00 | 119.45 | |
| 1177-78 | 1,893.46 | 94.67 |
| 3,468.13 | 173.41 | |
| 1273-78 | 2,436.15 | 121.80 |
| 3,586.72 | 179.34 | |
| 1306-78 | 1,458.26 | 72.91 |
| 2,417.25 | 120.86 | |
| 1307-78 | 3,069.03 | 153.45 |
| 4,785.27 | 239.26 | |
| 1308-78 | 1,094.02 | 54.70 |
| 1,796.92 | 89.85 | |
| 1318-78 | 3,338.67 | 166.93 |
| 3,734.84 | 186.74 | |
| 1319-78 | 2,625.13 | 131.26 |
| 2,965.65 | 148.28 | |
| 1407-78 | 1,458.07 | 72.90 |
| 3,158.80 | 157.94 | |
| 1408-78 | 1,940.00 | 97.00 |
| 2,850.45 | 142.52 | |
| 1421-78 | 3,846.95 | 192.35 |
| 3,998.02 | 199.90 | |
| 1422-78 | 1,792.72 | 87.64 |
| 2,536.50 | 126.83 | |
| 1480-78 | 3,301.36 | 165.07 |
| 2649-78 | 1,452.98 | 72.65 |
| 1,680.58 | 84.03 | |
| 3502-78 | 2,433.85 | 121.69 |
| 4,083.59 | 204.18 | |
| 4897-78 | 1,237.00 | 61.85 |
| 2,652.40 | 132.62 | |
| 5019-78 | 1,247.51 | 62.38 |
| 1,708.53 | 85.43 | |
| 5133-78 | 2,625.21 | 131.26 |
| 3,927.23 | 196.36 | |
| 5225-78 | 1,680.64 | 84.03 |
| 5226-78 | 2,840.00 | 142.00 |
| 2069-79 | 1,591.00 | 80.00 |
| 2,540.00 | 127.00 | |
| 2070-79 | 1,322.71 | 66.14 |
| 2,478.00 | 124.00 | |
| 3715-79 | 2,446.00 | 122.00 |
The issues in these consolidated cases are: (1) Whether any of the petitioners failed to report any part of the income received by them from tips and, if so, in what amounts, for the years in issue; and (2) whether petitioners are liable for the additions to tax under section 6653(a).
FINDINGS OF FACTS
Some of the facts in these cases were stipulated. The stipulations of facts and the exhibits attached thereto are incorporated herein by this reference.
Petitioners filed Federal income tax returns for the years in issue. At the time the petitions herein were filed, they resided in Las Vegas, Nevada.
During the years in issue, petitioners 5 were employed as waiters or waitresses by the MGM Grand Hotel (hereinafter*682 referred to as MGM or the employer). Respondent claims that they have understated the income that they received from tips while working in the Celebrity and Ziegfeld Romms of MGM.
The Celebrity Room was the main showroom where entertainers given prominent billing performed. Each night, two shows were presented in that room, an early show at which dinner was served and a later show at which only cocktails were served. In the Ziegfeld Room, which opened in April 1974, there were two presentations nightly of the stageshow, "Hallelujah Hollywood," and, beginning in March 1975, three presentations on Saturday nights. At all shows in the Ziegfeld Room, except on New Year's Eve, only cocktails were served.
Petitioners did not spend all of their working hours serving customers; they spent part of their time setting up the service areas, taking orders for food or drinks, and presenting checks. Each waiter or waitress who*683 worked in the Celebrity Room or Ziegfeld Room, however, spent the same proportion of his actual working hours serving customers as the other waiters and waitresses working in the same room.
Petitioners received tips in cash from customers. Theyalso received tips in cash from the hotel which were attributable to slips signed by customers on which they had included tips to be charged to their hotel bills or their credit card accounts. Petitioners also served customers who had purchased individual or group tour packages, which included show and drink coupons. These coupons included a gratuity for the waiter or waitress, usually equal to 15 per cent of the cost of the show, exclusive of tax, which the waiter or waitress received upon presentation of the coupons to the cashier. Only those tips declared by petitioners to the employer were reported on their W-2 forms.
During 1974 and 1975, there were 548,207 and 567,904 people, respectively, served in the Celebrity Room.
The seating area in the Celebrity Room comprised 30 stations. The seating capacities of the stations ranged from 35 to 52 customers, and the seating capacity of the entire room was approximately 1,200 people. During*684 the dinner show, waiters and waitresses assigned to each station worked in two-person teams, with one team waiting upon the tables served by that station. The work schedule was so arranged that one waiter or waitress of each team was scheduled to remain at the same station for the cocktail show, while the other one was scheduled to work only during the dinner show, on alternate evenings. Each waiter and waitress in the Celebrity Room was scheduled to rotate among the various stations in such a manner that, normally, he or she had an opportunity to work at each of the 30 stations during a six week period. On the first day of the week that a waiter or waitress was scheduled to work, he or she was assigned to a station in the area nearest to the stage. As the week progressed, he or she was assigned to areas further away from the stage. When the Celebrity Room was not filled to capacity, stations in the back of the room were closed and the waiters and waitresses assigned to them were relieved from duty. In accordance with the contract between the union of culinary workers and MGM, waiters or waitresses were guaranteed pay for four shifts of at least six hours each during each week. *685 They were, therefore, paid for the hours that they were scheduled to but not required to work, if they had not worked the number of hours for which they were guaranteed pay. The hours for which petitioners were dismissed from work, but were paid for working, were reflected in the payroll records of MGM as hours worked. MGM maintained no records indicating only the number of hours that waiters and waitresses actually worked.
The total number of customers served in the Ziegfeld Room was 504,052 in 1974 and 798,384 in 1975.
The Ziegfeld Room had a seating area divided into tiers, which contained 35 stations. It had a total seating capacity of 860 people, and the capacities of the stations ranged from28 to 44 customers. Each waiter and waitress in the Ziegfeld Room was assigned, under a rotation system, to work at each of the stations. The waiters and waitresses did not work as teams in the Ziegfeld Room. At the end of a rotation, a waiter or waitress was assigned, for a two-week period, to substitute for others who were absent. The Ziegfeld Room was generally filled to capacity.
Under the union contract, stations for waiters and waitresses were required to be rotated equitably*686 every day. The stations were in fact rotated equitably each day.
Those petitioners who worked in the Celebrity Room pooled the tips received for the dinner show with their station partners. Most of the petitioners gave approximately 15 per cent of the tips received for the night to the busboy who had assisted them. In addition, petitioners gave a few dollars per evening to other personnel, among whom were the bartender and barboy and a head busboy in the Ziegfeld Room.
At the trial of this case, only petitioners Michell, Sanger, Roger, and Sheffield submitted diaries purporting to contain a record of tips received by them. Petitioner Michell's diaries contain an entry for a date that does not exist (September 31, 1974) and do not contain an entry for a date that does exist (August 31, 1975), despite her testimony that she maintained her records on a daily basis. Petitioner Sanger submitted a tip diary only for the taxable year 1975. Although he apparently computed the amount of tips to declare to the employer each month from this diary and then made adjustments for any errors that he made in declaring tips when he filed his tax return, there are discrepancies between the*687 amounts of tip income shown in his diary for several months and the amounts of tip income that he reported to his employer for those months. Moreover, he reported no additional tips on his tax return for 1975 to adjust for the discrepancies between the amounts shown in his diary and the amounts declared to his employer.
Petitioner Roger's tip diaries indicate that he received net tip income, after making payments to busboys and bartenders, in the amounts of $ 2,045 from January 1974 to June 1974, $ 3,468 from July1974 to December 1974, and $ 8,270 from January 1975 to December 1975. According to his payroll history sheets, he worked 828 hours in the Celebrity Room from January 1974 to June 1974, 1,038 hours in the Ziegfeld Room from July 1974 to December 1974, and 2,063 hours in the Ziegfeld Room from January 1975 to December 1975. Thus, the tips recorded in his diary for each time period indicate that he received tips at the rate of $ 2.47 per hour from January 1974 to June 1974, $ 3.34 per hour from July 1974 to December 1974, and $ 4.01 per hour from January 1975 to December 1975.
Petitioner Sheffield did not prepare her diaries on a daily basis. For 1974, she kept worksheets*688 on which she indicated each night how much she had earned in tips together with one or two other persons with whom she worked for that night. At the end of each month, she divided each of the amounts on the worksheet by two or three, depending on how many others had worked together with her as a team on that particular night, to determine her own tip income. She, then, recorded those amounts in the diary submitted for 1974. She disposed of the worksheets at the end of the year. For the year 1975, she recorded her tips daily on pieces of paper. Then, at the end of each week, she copied the amounts that she had recorded on the pieces of paper into the diary for 1975 that she submitted at the trial. None of the other petitioners submitted tip records, although many of them claim that the amount reported on their returns accurately reflects the amount of tips that they earned.
Charged sales include sales made to customers who used credit cards to pay their bills, to those who requested that the charges be included on their hotel bills, and to those who purchased group or individual tour packages. During 1974 and 1975, charged sales constituted 29 percent and 31 per cent, respectively, *689 of total sales in the Ziegfeld Room. They constituted 38 per cent and 39 per cent of total sales in the Celebrity Room in 1974 and 1975, respectively. Tips on charged sales paid by the MGM cashier to waiters and waitresses are hereinafter referred to as paid-out tips.
The average hourly rate of paid-out tips for all waiters and waitresses in the Ziegfeld Room, derived by dividing the total number of hours shown on the payroll records as having been paid for into the total amount of tips paid out to them by the MGM cashier, was $ 3.28 in 1974 and $ 3.89in 1975. In the Celebrity Room, using the same method of computation, the average hourly rate of paid-out tips was $ 3.76 in 1974 and $ 3.64 in 1975. As indicated above, these hourly rates of "paid-out" tips do not include any part of the tips received by waiters and waitresses directly from the customers in cash. They reflect only tips charged to customers' bills in one form or another.
Those petitioners who worked in the Ziegfeld Room reported total tips received which result in average hourly tip rates in that room as follows:
| Petitioner | 1974 | 1975 |
| S. Powers (Belcher) | $ 3.02 | $ 3.02 |
| F. Belcher | $ 2.11 | $ 1.59 |
| Johnson | $ 1.73 | $ 1.86 |
| Michell | $ 2.54 | $ 3.26 |
| Nieto | $ 1.68 | $ 2.75 |
| Costa | $ 3.61 | $ 4.05 |
| Woods | $ 1.35 | $ 1.40 |
| Sheffield | 6 | |
| Fraginals | $ 2.49 | $ 3.84 |
| Dunlap | $ 2.44 | $ 3.10 |
| Limon | $ 2.57 | $ 2.73 |
| Villalvazo | $ 2.50 | $ 2.60 |
| Roger | $ 3.34 | $ 4.00 |
| Whiddon | 7 | |
| Sanger | $ 2.68 | $ 2.75 |
| Diaz | $ 2.67 | $ 4.76 |
| Reid | $ 2.50 | $ 2.78 |
The average hourly tip rates fro the Celebrity Room as reported by those petitioners who worked in it are as follows:
| Petitioner | 1974 | 1975 |
| Montano | $ 1.70 | 8 $ 2.25 |
| Sheffield | $ 3.24 | |
| Giuliano | $ 2.00 | $ 1.75 |
| Lucero | $ 0.73 | |
| Sanchez | $ 2.32 | $ 1.93 |
| Kelley | $ 2.42 | $ 1.88 |
| Kadmiri | $ 1.55 | $ 1.84 |
| Longworth | $ 1.90 | $ 1.78 |
| Whiddon | $ 0.98 | |
| Roger | $ 2.47 |
Comparing the tip rate per hour derived from petitioner Roger's*691 purported tip diary with the average hourly rates of tips paid out by the employer causes us to conclude that his diaries do not accurately reflect his tip income. Petitioners Michell, Sanger, and Sheffield also did not submit accurate, contemporaneously kept tip diaries. The total tips reported by each of the petitioners did not accurately reflect his or her tip income, as is evinced by a comparison of the average tip rates reported per hour by each petitioner with the average hourly rate of tips paid out by the employer.
Respondent computed income from tips of the several petitioners under a method which, in his opinion, does clearly reflect their income from this source. The petitioners dispute the reasonableness and substantial correctness of his method.
Respondent's method for the computation of income from tips consists of two parts. First, he determined a tip percentage for each room. Then, he computed a tip rate per hour for each room. He used those rates to determine each petitioner's tip income.
To determine the tip percentage for each room, respondent selected what is known as a stratified random sample of 52 days 9 for 1974, based upon the recommendation of*692 professional statisticians, for which he directed his agents to compute the total tips included on Master Charge charge slips, on American Express charge slips, and on front office charges. 10 Front office charges consist of charges included on hotel room bills, charges included on a single check for a large group (for example, 300 to 400) of customers, and charges for show and drink coupons. In 1975, the same types of charges were examined. The sample size, however, was decreased to 12 days for both rooms, based on the statisticians' advice that, if the results of those samples indicated that there was no significant difference in the tip percentages from those for 1974, then the sample size was sufficient. The tip percentage, computed by dividing the total amount of sales, including taxes, examined by the total tips charged with those sales, was as follows:
*693
| Ziegfeld Room | Celebrity Room |
| 1974 - 15% | 1974 - 14% |
| 1975 - 13% | 1975 - 14% |
Next, respondent made a tip rate per hour computation. Making this computation required that respondent adjust the sales figures which were available in MGM's accounting records. MGM's books of account indicated the total amounts of food and beverage sales, net of taxes, as follows:
| Ziegfeld room | Celebrity Room |
| 1974 - $ 5,380,474 | 1974 - $ 7,823,254 |
| 1975 - $ 9,472,292 | 1975 - $ 9,036,144 |
Respondent increased these figures by 13.5% for sales and entertainment taxes to determine gross sales. He, then reduced gross sales by 20% to account for nontippers (referred to by waiters and waitresses as "stiffs") and other factors, such as low tippers and those customers who left without paying their bills, to arrive at adjusted sales figures on which tips could be expected. Respondent, then, multiplied the adjusted sales figures by the applicable tip percentages to compute gross tips. He reduced gross tips by 16.67% for amounts paid by waiters and waitresses to busboys, bartenders, and other personnel. Finally, he divided the resulting figure, adjusted tips, by the total number*694 of hours for which waiters and waitresses were paid for working in each room for the year. This final computation generated tip rates per hour, as follows:
ZiegfeldRoom
1974
adjusted tips / hours paid = $ 610,660 / 74,852 = $ 8.16
1975
adjusted tips / hours paid = $ 931,720 / 102,308 = $ 9.11
Celebrity Room
adjusted tips / hours paid = $ 828,710 / 116,784 = $ 7.10
adjusted tips / hours paid = $ 957,191 / 117,535 = $ 8.14
Respondent multiplied the number of hours worked by each employee by the applicable tip rates per hour to determine each petitioner's tip income.
To ascertain the correct amount of adjustment for stiffs and other factors, respondent's agent interviewed seven employees of MGM. Two of these employees were not waiters or waitresses, but captains. They were chosen by the agent upon the basis of the large number of hours that they worked or the large amount of tips that they reported, although he could not recall the criteria. The agent, then, determined, from the responses of the employees interviewed, that 20 per cent was a reasonable estimate. This method of determining the adjustment figure did not strictly comply with the requirements*695 of the scientific method, since the sample was not of a sufficient size and apparently the persons to be interviewed were not chosen at random.
After respondent issued the statutory notices of deficiency to petitioners, but prior to the trial of the instant cases, he became aware of the three errors in his computations of the deficiencies. He admitted these errors at trial.
First, respondent learned that the MGM business records to which he referred to ascertain how many hours each petitioner was paid in connection with his work in a particular room only indicated where he or she had worked at the end of the year. Sincework locations of several petitioners changed during the year, the number of hours paid at a specific location used by respondent initially to determine the amount of their deficiencies was incorrect. Respondent has introduced into evidence payroll history sheets, showing the correct number of hours paid for work in the Celebrity Room and Ziegfeld Room of each petitioner. For the years in issue, petitioners were paid for the following number of hours (excluding vacation and sick leave but including the overtime hours they actually worked) in connection with*696 their work in the Ziegfeld and Celebrity Rooms:
| Petitioners | Year | Location | Total Hours |
| Sandra L. Powers (Belcher) | 1974 | Ziegfeld | 1,242 |
| 1975 | 1,777 | ||
| Fred N. Belcher | 1974 | Ziegfeld | 1,346 |
| 1975 | 957 | ||
| Robert E. Johnson | 1974 | Ziegfeld | 1,270 |
| 1975 | 1,173 | ||
| Osvaldo Montano | 1974 | Celebrity | 1,624 |
| 1975 | 1,683 | ||
| 1976 | 1,612 | ||
| Martine M. Michell | 1974 | Ziegfeld | 1,324 |
| 1975 | 1,987 | ||
| Antonio M. Nieto | 1974 | Ziegfeld | 1,772 |
| 1975 | 2,165 | ||
| Joseph Costa | 1974 | Ziegfeld | 1,322 |
| 1975 | 1,692 | ||
| Mary F. Woods | 1974 | Ziegfeld | 876 |
| 1975 | 2,139 | ||
| Sharron I. Sheffield | 1974 | Celebrity | 1,504 |
| 1975 | Celebrity | 1,033 | |
| 1976 | Ziegfeld | 864 | |
| EvelioP. Fraginals | 1974 | Celebrity | 664 |
| 1975 | Ziegfeld | 1,340 | |
| 1976 | 2,203 | ||
| Dottie M. Dunlap | 1974 | Ziegfeld | 1,412 |
| 1975 | 1,975 | ||
| Lonnie Limon | 1974 | Ziegfeld | 1,188 |
| 1975 | 2,069 | ||
| Alejandro Villalvazo | 1974 | Ziegfeld | 1,390 |
| 1975 | 1,969 | ||
| June L. Giuliano | 1974 | Celebrity | 1,546 |
| 1975 | 1,540 | ||
| Pierre Roger | 1974 | Celebrity | 828 |
| 1974 | Ziegfeld | 1,038 | |
| 1975 | 2,063 | ||
| Rosalie Lucero | 1975 | Celebrity | 1,524 |
| Hadji M. Kadmiri | 1974 | Clebrity | 1,422 |
| 1975 | Celebrity | 1,320 | |
| 1975 | Ziegfeld | 86 | |
| Betty B. Whiddon | 1974 | Celebrity | 1,590 |
| 1975 | Celebrity | 948 | |
| 1975 | Ziegfeld | 822 | |
| Robert Sanger | 1974 | Ziegfeld | 1,388 |
| 1975 | 1,923 | ||
| James K. Longworth | 1974 | Celebrity | 1,416 |
| 1975 | 1,498 | ||
| Miquel A. Diaz | 1974 | Ziegfeld | 1,404 |
| 1975 | 2,078 | ||
| Charles H. Reid | 1974 | Ziegfeld | 1,354 |
| 1975 | 1,937 | ||
| Bernardo Sanchez | 1974 | Celebrity | 1,466 |
| 1975 | 1,642 | ||
| Mary Ann Kelley | 1974 | Celebrity | 1,332 |
| 1975 | 1,640 |
*697 In some cases, if the tip rates that respondent originally determined are used with the correct total hours paid for at each location, deficiencies result which are greater than those stated in the notices of deficiency. Respondent has not asserted claims therefor, although he has acknowledged that correcting the hours paid for at each location results in decreased deficiencies in other cases. Since the respondent has not asserted claims for increased deficiencies, this Court is without jurisdiction to determine deficiencies greater than those set forth in the statutory notices of deficiency. Section 6214(a). Consequently, if the Rule 155 computations required by our opinion herein result in deficiencies greater than those in the notices of deficiency because of the correction of hours worked at each location, the additional amounts shall not be assessed.
Second, respondent discovered that the amount of gross sales, as he had computed it, did not reflect the excess of minimum charges over actual sales. The actual gross sales, including taxes, are:
| Ziegfeld Room | Celebrity Room |
| 1974 - $ 7,946,447 | 1974 - $ 9,951,479 |
| 1975 - $ 13,130,213 | 1975 - $ 11,196,126 |
*698 Third, an analysis made by respondent's statisticians, two weeks before the trial of the instant cases, revealed that there was a significant difference between the 1974 and 1975 percentages of tips on the front office charges examined by his agents. Upon investigation, he determined that the reason for this significant difference was that MGM had changed its method of accounting for coupon sales sometime during the early part of 1975. The tip percentages originally calculated by respondent for 1974 and 1975 appear greater than they actually are because of MGM's method of accounting for coupon sales in 1974 and the early part of 1975. Respondent, therefore, has recomputed tip percentages for those years by eliminating the front office charges, thus using only the Master Charge and American Express portion of his analysis, to determine the actual tip percentages. This new computation would result in tip percentages being used in respondent's tip formula computations as follows:
| Ziegfeld Room | Celebrity Room |
| 1974 - 12.9% | 1974 - 13.0% |
| 1975 - 12.8% | 1975 - 13.5% |
Using the actual amounts of gross sales, including taxes, and the tip percentages as recomputed by*699 respondent in his formula would cause the tip rates per hour to be:
| Ziegfeld Room | Celebrity Room |
| 1974 - $ 9.13 | 1974 - $ 7.38 |
| 1975 - $ 10.95 | 1975 - $ 8.57 |
Respondent has not filed a claim for the increased deficiencies that would result from application of these increased tip rates.
The tip rates per hour for each waiter and waitress, after making adjustments to respondent's formula with respect to the tip percentages on charge and noncharge sales and the percentages of charge and noncharge sales on which patrons gave no tip, left without paying their bills, etc., are as follows:
| Ziegfeld Room | Celebrity Room |
| 1974 - $7.34 | 1974 - $ 6.15 |
| 1975 - $ 8.51 | 1975 - $ 7.10 |
OPINION
Section 6001 and the regulations thereunder require taxpayers to keep such tip records as may be prescribed by the Secretary of the Treasury. If a taxpayer's records do not accurately reflect his income, or if he keeps no records, respondent is authorized to compute his taxable income under a method which, in his opinion, does clearly reflect income. Section 446(b); Meneguzzo v. Commissioner, 43 T.C. 824">43 T.C. 824, 831 (1965).*700
Petitioners attack respondent's formula method of computing their tip income as unreasonable and not substantially correct, claiming that he has failed to adhere to accepted statistical (or scientific) sampling methods which require, among other things, that the statistician choose a sample of a size sufficient to reduce the risk of generating an unrepresentative sample, that he choose items or persons to be sampled in a random fashion, that inferences from the sample data be applied only to the population from which the sample was drawn, and that surveys, when called for, be administered in such a manner as to reduce the risk of nonsampling error. 11 Respondent replies that his agents were only attempting to use the scientific method to ascertain the average percentage of tips charged on charge sales and that it is not incumbent upon him to produce a statistically precise result when reconstructing the tip income of petitioners. We agree that respondent is not required to achieve a statistically precise reconstruction of petitioners' tip income. He is, furthermore, not required to use only accepted statistical sampling methods.
*701 The ultimate question is the correctness of respondent's determination of the amount of tip income earned by petitioners considering the record as a whole, and not merely in light of a formula used by respondent to compute the amounts determined. 12
Petitioners had a legal duty to keep records from which their tip income could be accurately ascertained. Havingfailed to comply with this duty, they cannot now, by reason of their laxity, impose a duty upon respondent to produce statistically precise estimates of their tip income. Neithercan they frustrate reasonable attempts by the Commissioner to determine their tip income by compelling investigation and recomputation under every possible method of determination. Cf. Webb v. Commissioner, 394 F.2d 366">394 F.2d 366 (5th Cir. 1968).
Although respondent's determinations by formula may not be expected to be exact, they are expected to be substantially correct. Anson v. Commissioner, 328 F.2d 703 (10thCir. 1964).*702 As a general rule, they are deemed presumptively correct, however, and the taxpayers have the burden of proving them arbitrary or erroneous. Welch v. Helvering, 290 U.S. 111 (1933); Rule 142, Tax Court Rules of Practice and Procedure. The respondent's admissions of error do not cause his determination to be arbitrary and capricious and, hence, do not deprive it of its usual presumption of correctness. Mensik v. Commissioner, 37 T.C. 703">37 T.C. 703 (1962), affd. 328 F.2d 147">328 F.2d 147 (7th Cir. 1964), cert. denied 379 U.S. 829">379 U.S. 829 (1964).
Respondent asserts that, since the method that he used to determine petitioners' tip income is essentially the same as the methods approved in Mendelson v. Commissioner, T.C. Memo. 1961-319, affd. 305 F.2d 519">305 F.2d 519 (7th Cir. 1962), cert. denied 371 U.S. 877">371 U.S. 877 (1962); Meneguzzo v. Commissioner, supra; and Cracchiola v. Commissioner, T.C. Memo.1979-3, his determination is not arbitrary. In these cases, this Court did approve methods quite similar to that used by respondent to determine tip income; however, as made evident in at least the *703 Mendelson and Meneguzzo cases, the Court will, where necessary, make adjustments to respondent's determinations of tip income made by a formula. Indeed, respondent acknowledges, in his reply brief, "there are aspects of a tip formula which may be subject to adjustment."
In the Meneguzzo case respondent established a ratio of tips per dollar of salary, but then reduced that ratio and used the reduced amount to compute the taxpayer's tip income. It was this Court's opinion that respondent's reduction, for possible variations in tip income caused by differences in station location, efficiency, etc., was ample. In Mendelson v. Commissioner, supra, it was decided that application of a ten per cent tip rate to food and beverage sales was more appropriate than application of the 12 per cent tip rate determined by respondent. Although the Court of Appeals agreed that respondent's method of determining tip income was within his statutory authority and was not arbitrary, excessive, or without rational foundation, it affirmed this Court's reduction of the tip percentage.
We find that respondent's determinations herein were not arbitrary, when considered*704 in light of the broad statutory power granted him to compute petitioners' taxable income under a method which, in his opinion, does clearly reflect their income.
Thereare three major areas in which petitioners dispute the correctness of figures used by respondent and in which we have considered making adjustments: (1) Petitioners dispute respondent's application to all sales of the average tip percentage determined by respondent by using only tips charged by customers to their bills; (2) petitioners dispute respondent's reduction of gross sales for nontippers and other factors by only 20 per cent, claiming a greater reduction should have been made; and (3) petitioners dispute respondent's reduction of gross tips by the fixed per cent 16.67 to account for amounts paid by petitioners to busboys, bartenders, and other personnel, relying on the opinion of their expert witness to the effect that a percentage and a constant cannot be combined to derive a fixed per cent. The evidence adduced at trial convinces us that adjustments are necessary to arrive at a result which will be fair to petitioners. accordingly, based on all the evidence, we have made adjustments to respondent's formula.*705 Our findings of fact reflect the result of such adjustments.
Petitioners assert that, since MGM's payroll records reflected hours for which many employees, especially in the Celebrity Room, received pay but did not actually work and, thus, did not have an opportunity to receive tips, basing the tip percentages on total hours worked as recorded in those records causes grossly inaccurate results. Petitioners' criticism of respondent's use of total number of hours worked as recorded in MGM's records shows a misconception of the way the formula operates. Although several of the petitioners testified as to the widely varying numbers of days for which they were paid, without working, no petitioner presented an accurate, contemporaneously kept record indicating just now many such days there were. The stations in the Celebrity Room were rotated equitably, with each waiter or waitress being assigned to a station in the front tier at the beginning of his work week and being assigned to stations further and further back as his work week progressed. Since petitioners presented no corroborating evidence to the contrary, it is reasonable to assume that, for every petitioner who worked in*706 the Celebrity Room, the ratio of hours paid for but not worked to the total number of hours paid for was the same. If the number of hours actually worked by all waiters and waitresses in the Celebrity Room had been known and had been used in the computation, a higher tip rate per hour would naturally have resulted. Multiplying that higher tip rate per hour by the number of hours appearing on each petitioner's payroll record, less the proportional number of hours not worked, would result in essentially the same amount of tips being allocated to each employee.
Respondent used the average hourly tip rates that he determined for 1975 to compute petitioner Montano's tip income for 1976. Petitioners have not presented any proof or arguments to show this approach incorrect. Since respondent's determination is presumptively correct, unless petitioners have met their burden of proving it otherwise, we uphold respondent's application of the 1975 tip rates, as herein modified, to determine petitioner Montano's 1976 deficiency. Welch v. Helvering,supra; Rule 142, Tax Court Rules of Practice and Procedure.
Respondent has imposed additions to tax under section 6653(a)*707 in all of the cases consolidated herein. Section 6653(a) provides for an addition to the tax, equal to five per cent of the underpayment, where any part of an underpayment is due to negligence or intentional disregard of rules and regulations. Petitioners have failed to show that their negligent disregard of section 6001 and the regulations thereunder was not the cause of their substantial understatements of tip income. We, therefore, sustain the respondent's imposition of the additions to tax. Meneguzzo v. Commissioner, supra at 836; Schroeder v. Commissioner, 40 T.C. 30">40 T.C. 30, 34 (1963).
To reflect the foregoing and allow for concessions agreed upon among some of the parties,
Decisions will be entered under Rule 155.
Footnotes
1. Cases of the following petitioners are consolidated herewith; Fred N. Belcher, docket No. 815-78; Fred N. Belcher and Sandra L. Belcher, docket No. 816-78; Robert E. Johnson and Soccorro E. Vidro Johnson, docket No. 1004-78; Osvaldo Montano, docket No. 1015-78; Martine M. Michell, docket No. 1177-78; Antonio M. Nieto, docket No. 1273-78; Joseph Costa, docket No. 1306-78; Mary F. Woods, docket No. 1307-78; Sharron I. Sheffield, docket No. 1308-78; Evelio P. Fraginals, docket No. 1318-78; Dottie M. Dunlap, docket No. 1319-78; Lonnie Limon and Zenaida Limon, docket No. 1407-78; Alejandro Villalvalzo and Guadulupe Villalvalzo, docket No. 1408-78; Salvatore Giuliano and June L. Giuliano, docket No. 1421-78; PierreRoger and Rita R. Roger, docket No. 1422-78; Albert G. and Rosalie Lucero, docket No. 1480-78; Hadji M. Kadmiri and Judith I. Kadmiri, docket No. 2649-78; Chester R. Whiddon and Betty B. Whiddon, docket No. 3502-78; Robert Sanger, docket No. 4897-78; James K. Longworth and Mary Ann Longworth, docket No. 5019-78; Miguel A. Diaz and Felicia N. Diaz, docket No. 5133-78; Charles H. Reid, docket No. 5225-78; Charles H. Reid and Vikki D. Reid, docket No. 5226-78; Bernardo Sanchez,docket No. 2069-79; Mary Ann Kelly, docket No. 2070-79; Osvaldo Montano, docket No. 3715-79.↩
2. All section references are to the Internal Revenue Code of 1954, as amended, unless otherwise indicated. ↩
3. Pursuant to the order of assignment, on the authority of the "otherwise provided" language of Rule 182, Tax Court Rules of Practice and Procedure↩, the post-trial procedures set forth in that rule are not applicable to this case.
4. Mary Ann Longworth is the widow of James K. Longworth, who was employed in the Celebrity Room of the MGM Grand Hotel during their 1974 and 1975 taxable years. Mr. Longworth died after filing the petition in this case. The case as to petitioner James K. Longworth has been dismissed for lack of prosecution, but a decision will be entered as to him for the same amounts and years as for petitioner Mary Ann Longworth, pursuant to an order dated August 12, 1980.↩
5. Theissues in these cases relate only to the petitioners who were employed in the Ziegfeld Room or Celebrity Room of the MGM Grand Hotel. In cases where joint returns were filed, therefore, the term petitioner will have reference only to such petitioners.↩
6. Petitioner Sheffield worked in both rooms in 1975. For that year, she declared tips on her return, in addition to those she had declared to her employer. The record does not indicate in which room the additional tips that she reported were earned. It is, therefore, impossible to allocate the additional tips reported between the time she worked in each room. ↩
7. PetitionerWhiddon's circumstances for 1975 are similar to those of petitioner Sheffield, thus making it impossible to determine in which room she earned the additional tips that she reported.↩
8. The correct amount of petitioner Montano's tip income is also in issue for the year 1976. That year he reported tips at an average hourly rate in the amount of $ 2.55.↩
9. Since the Ziegfeld Room did not open until April 1974, the random sampling technique resulted in charge slips being examined for 35 days, rather than 52, for the Ziegfeld Room in 1974. ↩
10. Credit card slips with no tip on them or with a tip greater than 50 per cent of the bill, were not examined, based on the advice of respondent's statisticians. According to them, a slip with no tip on it would provide no information as to what occurred, since a tip may have been left in cash and a slip with a tip greater than 50 per cent would be so unusual as to bias the results.↩
11. Nonsampling error is caused when incorrect answers are received. In an interview survey, for example, this may occur if the persons interviewed, as a result of intimidation, answer questions falsely.↩
12. See Steiner v. Commissioner,T.C. Memo. 1963-143; Williams v. Commissioner, T.C. Memo. 1963-30↩.