Question

It is interesting to determine whether the rates of a hotel in Los Angeles, Atlanta, Houston, and Phoenix are the same or not. Seven hotels are sampled in Los Angeles, five hotels are sampled in Atlanta and Houston, while six hotels are sampled in Phoenix. Data are not reported, only the mean and standard deviation for each city are given for statistical analysis.

	Los Angeles	Atlanta	Houston	Phoenix
Mean	229.14	190	195	231.33
Standard Deviation	19.71	6.67	4.12	17.56

A) State the Null and alternative hypothesis you are testing

B) Compute the respective SS and fill in the ANOVA table to summarize the comparison.

C) Based on the F value, what is your conclusion, use a= 0.025. What is the best you can say about the P value based on the F tables.

D) Find the 95% confidence interval’s for the true average of Los Angeles and Atlanta.

Answer 1

It is interesting to determine whether the rates of a hotel in Los Angeles, Atlanta, Houston, and Phoenix are the same or not. Seven hotels are sampled in Los Angeles, five hotels are sampled in Atlanta and Houston, while six hotels are sampled in Phoenix. Data are not reported, only the mean and standard deviation for each city are given for statistical analysis.

	Los Angeles	Atlanta	Houston	Phoenix
Mean	229.14	190	195	231.33
Standard Deviation	19.71	6.67	4.12	17.56

A) State the Null and alternative hypothesis you are testing

H1: At least one pair of population means are different

B) Compute the respective SS and fill in the ANOVA table to summarize the comparison.

Group	Mean	SD	n	Total		SSGroups	SSError
1	229.14	19.71	7	1603.98		1651.320214	2330.9046
2	190	6.67	5	950		2827.648786	177.9556
3	195	4.12	5	975		1763.605308	67.8976
4	231.33	17.56	6	1387.98		1847.831874	1541.768

ANOVA
Source	df	SS	MS	F	P-value
Groups	3	8090.406	2696.802	12.44116	0.0001
Error	19	4118.526	216.7645
Total	22	12208.93

C) Based on the F value, what is your conclusion, use a= 0.025. What is the best you can say about the P value based on the F tables.

Critical F(3,19) at 0.025 level=3.903

Calculated F=12.44 which is > critical F =3.903. Ho is rejected.

P value =0.0001

D) Find the 95% confidence interval’s for the true average of Los Angeles and Atlanta.

Critical t at 5% level=2.093

95% CI for mean difference = mean difference ± t*sqrt(MSE*(1/n1+1/n2))

=(229.14-190) ± 2.093*sqrt(216.7645*(1/7+1/5))

Lower limit = 39.14 -2.093*8.6209 =21.09646

upper limit = 39.14 +2.093*8.6209 =57.18354