Question

6) 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 10% with 12 degrees of freedom.

	ITALIAN	SEAFOOD	STEAKHOUSE
SAMPLE MEAN	14	17	20

6.A) What is the critical value for the given level of confidence?

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

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

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

6.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?

6.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 the t statistic at significance level = 0.01 and degree of freedom = n₁+n₂-2 = 5 + 5 - 2 = 8 is obtained using the t critical value table.

b)

The t statistic is obtained using the formula,

Where, standard error,

Now, the t statistic comparing A&B

c)

The t statistic comparing A&C

d)

The t statistic comparing B&C

e)

Comparison	|t statistic|		|t critical|	Decision
A&B	1.1339	<	2.8965	Do not reject Null hypothesis
A&C	2.2678	<	2.8965	Do not reject Null hypothesis
B&C	1.1339	<	2.8965	Do not reject Null hypothesis

f)

All the means are same at 1% significance level.