A resort area has three seafood restaurants, which employ students during the summer season. The local chamber of commerce took a random sample of five servers from each restaurant and recorded the tips they received on a recent Friday night. The results (in dollars) of the survey are shown in the table below. Assume that the Friday night for which the data were collected is typical of all Friday nights of the summer season. Barzini’sHwang’sJack’s9767931148510210592988578801209091 Based on the above data, a one way ANOVA analysis was performed and the results are shown below. Anova: Single Factor SUMMARY GroupsCountSumAverageVariance Barzini's5521104,2191,7 Hwang's541282,4103,3 Jack's546492,869,7 ANOVA Source of VariationSSdfMSFP-valueF critBetween Groups1188,9333332594,46666674,8900466140,027972363,88529383Within Groups1458,812121,5666667 Total2647,73333314 You are required to answer the following questions:Would a student seeking a server’s job at one of these three restaurants conclude that the mean tips on a Friday night are the same for all three restaurants? Use the 5% level of significance.If the sample data indicate the existence of mean tips on a Friday night across these three seafood restaurants, which restaurants appear to produce different average tips at 5% level? Hint: Construct an appropriate test for difference in all pairs of means.

The results (in dollars) of the survey are shown in the table below. Barzini’s Hwang’s Jack’s…

Answered: SUMMARY Groups Count Sum…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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A resort area has three seafood restaurants, which employ students during the summer season. The local chamber of commerce took a random sample of five servers from each restaurant and recorded the tips they received on a recent Friday night. The results (in dollars) of the survey are shown in the table below. Assume that the Friday night for which the data were collected is typical of all Friday nights of the summer season.

Barzini’s	Hwang’s	Jack’s
97	67	93
114	85	102
105	92	98
85	78	80
120	90	91

Based on the above data, a one way ANOVA analysis was performed and the results are shown below.

Anova: Single Factor

SUMMARY
Groups	Count	Sum	Average	Variance
Barzini's	5	521	104,2	191,7
Hwang's	5	412	82,4	103,3
Jack's	5	464	92,8	69,7


ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	1188,933333	2	594,4666667	4,890046614	0,02797236	3,88529383
Within Groups	1458,8	12	121,5666667

Total	2647,733333	14

You are required to answer the following questions:

Would a student seeking a server’s job at one of these three restaurants conclude that the mean tips on a Friday night are the same for all three restaurants? Use the 5% level of significance.
If the sample data indicate the existence of mean tips on a Friday night across these three seafood restaurants, which restaurants appear to produce different average tips at 5% level? Hint: Construct an appropriate test for difference in all pairs of means.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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