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 4 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 0.1

Italian            Seafood    Steakhouse

Sample Mean                24              24                27

Sample Variance 0.7 8.7 0.7

5.A) How many degrees of freedom are there in the problem?

5.B) What is the critical value for this problem?

5.C) What is the value for the mean of the means?

5.D) What is the value of SSTR and MSTR respectively?

5.E) What is the value of SSE and MSE respectively?

5.F) What is the value for the test statistic?

5.G) What is your decision after performing the test?

5.H) What is your conclusion after the test? Be specific and relate the conclusion to the problem.

Answer 1

Applying ANOVA on above data:

Group	ni	x̅i	S2i	ni*(Xi-Xgrand)2	(ni-1)*S2i
Italian	4	24	0.700	4.000	2.10
Seafood	4	24	8.700	4.000	26.10
Steakhouse	4	27	0.700	16.000	2.10
	grand mean=	25.0000		24.000	30.30
				SSTr	SSE
Source	SS	df	MS	F
between	24.00	2.000	12.0000	3.56
error	30.30	9.000	3.3667
total	54.30	11.0000

A)

degree of freedom for numerator =k-1=2

degree of freedom for denominator =N-k=12-3 =9

B ) critical value at 0.1 level and above degree of freedom =3.01

C) the value for the mean of the means =25.00

D) value of SSTR =24

MSTR =24/2 =12

E) SSE =30.30

MSE =30.3/9 =3.3667

F) alue for the test statistic =MSTR/MSE =3.56

G)

reject Ho as test statistic is higher than critical value

H) we have sufficient evidence to conclude that average meal price per person differs between three type of restaurants,