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 for collected data in dollars. The MSE value is 7. Allow for an error of 5% with 12 degrees of freedom. Italian Seafood Steakhouse Sample Mean 14 17 20

a What is the critical value for the given level of confidence?

b. What is the test statistic for means A & B ? (allow for a difference in values of + or - 0.01)

c. What is the test statistic for means A & C? (allow for a difference in values of + or - 0.01)

d. What is the test statistic for means B & C? (allow for a difference in values of + or - 0.01)

e. What is your decision (with respect to the null hypotheses) after performing the test for means A & B, A & C and B & C respectively?

f. What is your conclusion after performing these tests with regards to which is different and which is the same?

Answer 1

a. the critical value for an error of 5% with 12 degrees of freedom , we find the critical t value from the statistics table at confidence level

the critical value is

b. means A and B is given as

we get test statistic as

c. the mean for C is given as

the test statixtics for means A and C is

d. the test statistics for mean B and C is

e. since values of all test statistics we find above is less than critical value -1.7823 , so we reject the null hypothesis

f. after performing the test we conclude that population means of A,B and C are all different