Question

Another question in your restaurant survey was a Likert-type scaled question about likelihood of coming back to the restaurant (where 1 = completely disagree and 7 = completely agree). The question was:

X3: I would return to this restaurant (respond on a 1-7 scale).

The 50 respondents are grouped into three categories by residence: city, suburbs, or rural. The results are in the Excel spreadsheet “Customer Satisfaction Study Part 2.”   You think there might be a difference in the likelihood of returning based on where customers live, and you will do a statistical analysis to see if the difference is significant.

Part 1--State the null and alternate hypotheses in plain English sentences (not equations).

Part 2--Using Excel or any statistical package you are familiar with, do the appropriate statistical analysis to determine if these three categories are significantly different from each other. Clearly justify your choice of statistical analysis. Do a follow-up procedure, if required, to obtain further results. Print out the computer results.  

Part 3--Can you reject the null hypothesis? Why or why not? Make a brief statement to management that clearly summarizes your findings.

City	Suburbs	Rural
4	2	6
5	3	6
2	1	4
3	3	4
4	4	2
5	4	3
4	5	2
2	2	3
5	3	2
5	3	3
3	4	2
7	6	1
7	5	1
6	4	2
4	4
5	3
6
5

Answer 1

Answer:

Another question in your restaurant survey was a Likert-type scaled question about likelihood of coming back to the restaurant (where 1 = completely disagree and 7 = completely agree). The question was:

X3: I would return to this restaurant (respond on a 1-7 scale).

The 50 respondents are grouped into three categories by residence: city, suburbs, or rural. The results are in the Excel spreadsheet “Customer Satisfaction Study Part 2.”   You think there might be a difference in the likelihood of returning based on where customers live, and you will do a statistical analysis to see if the difference is significant.

Part 1--State the null and alternate hypotheses in plain English sentences (not equations).

Ho: There is no difference in the likelihood of returning based on where customers live

H1: There is a difference in the likelihood of returning based on where customers live

Part 2--Using Excel or any statistical package you are familiar with, do the appropriate statistical analysis to determine if these three categories are significantly different from each other. Clearly justify your choice of statistical analysis. Do a follow-up procedure, if required, to obtain further results. Print out the computer results.  

One factor ANOVA
	Mean	n	Std. Dev
	4.6	18	1.46	City
	3.5	16	1.26	Suburbs
	2.9	14	1.59	Rural
	3.7	48	1.57	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	22.11	2	11.053	5.33	.0084
Error	93.37	45	2.075
Total	115.48	47
Post hoc analysis
p-values for pairwise t-tests
		Rural	Suburbs	City
		2.9	3.5	4.6
Rural	2.9
Suburbs	3.5	.2841
City	4.6	.0027	.0384
Tukey simultaneous comparison t-values (d.f. = 45)
		Rural	Suburbs	City
		2.9	3.5	4.6
Rural	2.9
Suburbs	3.5	1.08
City	4.6	3.17	2.13
critical values for experimentwise error rate:
		0.05	2.42
		0.01	3.08

Part 3--Can you reject the null hypothesis? Why or why not? Make a brief statement to management that clearly summarizes your findings.

The calculated F(2,45) = 5.33 is > critical F( 2,45) at 5% level 3.204. Ho is rejected.

There is enough evidence to conclude there is a difference in the likelihood of returning based on where customers live. Post hoc test shows that Rural is significantly different from City.