Question

. A large bookstore chain needs to restock on comic books and wants to determine if customers have a preference for superhero. A random sample of 200 customers was asked who their favorite superhero was. Superhero preferences are recorded below. Use alpha = 0.01.

Batman	Superman	Wonder Woman	Spiderman	Ironman
68	22	42	42	26

Step 1: State your hypotheses (null and alternative) in words.

Step 2: Set up the criteria for making a decision. That is, find the critical value.

Step 3: Summarize the data into the appropriate test-statistic.

Step 4: Evaluate the null hypothesis (Reject or Fail to Reject).

Step 5: What is the interpretation of your findings (in words)?

Answer 1

Step 1:

Ho: Customers have no preference for superhero; i.e. proportion of customer prefering diff superheros is same =1/5= 0.20

Ha: Customers have preference for superhero; i.e. some proportion of customer prefering diff superheros is not as per Ho.

Step 2: Decision criteria:

Chi square critical = CHISQ.INV.RT(probability,df) = CHISQ.INV.RT( 0.01, 4) = 13.277

critical = 13.277

Rejection area: (Reject Ho for ,   > 13.277}

Step 3 Test statistics - Chi square Test for Goodness of fit

Positions	Observed values (fo)	Expected Proportions	Expected values (fe)	(fo-fe)2/ fe
Batman	68	0.200	40.0000	19.6000
superman	22	0.200	40.0000	8.1000
wonderwoman	42	0.200	40.0000	0.1000
spider man	42	0.200	40.0000	0.1000
iron man	26	0.200	40.0000	4.9000
Total	200	1.000	200.0000	32.8000

= 32.80

Step 4:

As the (32.80) is greater than critical (13.277), we reject the Null hypothesis.

Also as the p value (0.000001) is less than (0.01), we reject the Null hypothesis.

Step 5:

Hence we have sufficient evidence to believe that Customers have preference for superhero

i.e. Proportion of customer prefering diff superheros is not equal