PLEASE COMPLETE ALL PARTS OF THIS QUESTION A reporter with the Saint Pete Times
ID: 3376523 • Letter: P
Question
PLEASE COMPLETE ALL PARTS OF THIS QUESTION
A reporter with the Saint Pete Times is working on a story about the main factors making restaurants in the St. Pete area different from each other. The variable he is considering is the average meal price per person. The reporter selects a sample of 5 restaurants serving Italian food, Seafood and Steaks. The reporter believes that average price meal per person in the St Pete area is about the same independently of the type of restaurant. The table below shows sample mean and variances for collected data in dollars. Allow for an alpha of 0.01. Italian Seafood Steakhouse Sample Mean 14 17 20 Sample Variance 25 25 2.5 16Explanation / Answer
Solution:
a. Degrees of freedom, df = k - 1 = 3 - 1 = 2
Degrees of freedom, df = n- k = 15 - 3 = 12
Answer is (2, 12)
b. Using F-tables, the critical value at a = 0.01 is
F (0.01, 2, 12) = 6.93
c. Value of mean = (14 + 17 + 20)/3
Value of mean = 51/3 = 17
d. SSTR = 5 (14 - 17)^2 + 5 (17 - 17)^2 + 5 (20 - 17)^2
SSTR = 90
MSTR = SSTR/degrees of freedom
MSTR = 90/2
MSTR = 45
Answer is (90, 45)
e. SSE = (5-1)*2.5 + (5 - 1)*2.5 + (5 - 1)*16
SSE = 84
MSE = SSE/df
MSE = 84/12
MSE = 7
Answer is 84, 7
Solution:
f, Test Statistics
F= MSTR/MSE
F = 45/7
F = 6.43
g. Since F-statistics is less than the critical value, we fail to reject Ho.
Answer is accept the null.
h. We can conclude that there is no difference between the average price meal per person in St Pete area.
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