Question

A market researcher randomly selected 1000 customers to study the relationship between gender and the book category they preferred most (Romance, Non-Fiction, Adventure, Fantasy) in which customers prefer to read. The results are summarized in the following contingency table:

	Romance	Non-Fiction	Adventure	Fantasy	Total
Male	80	170	150	110	510
Female	100	130	130	130	490
Total	180	300	280	240	1000

Suppose the researcher would like to test whether gender is related to the book category they prefer. If an appropriate hypothesis test is carried out, state the null and alternative hypotheses.

Select one:

a. H₀: Gender and preferred book category are dependent.
H_A: Gender and preferred book category are independent.

b. H₀: The number of males/females who prefer each book category is the same.
H_A: The number of males/females who prefer each book category is not the same.

c. H₀: The distribution of female customers preferring each book category is not the same as the distribution of male customers preferring each book category.
H_A: The distribution of female customer preferring each book category is the same as the distribution of male customers preferring each book category.

d. H₀: The number of individuals who prefer each book category is the same.
H_A: The number of individuals who prefer each book category is not the same.

e. H₀: Gender is independent of the preferred book category.
H_A: Gender is not independent of the preferred book category.

Answer 1

For the above problem the appropriate hypothesis is represented by option e, that is

H0: gender is independent of preferred book category.

H1: gender is not independent of preferred book category.

The above problem is solve using minitab the output of minitab is attached below,

P value= 0.017, alpha = 0.05

As P value < alpha, null hypothesis is rejected at 5 % level of significance.

Therefore, we conclude that Gender is not independent of the preferred book categorycategory, at 5% level of significance.

As level of significance change result might be different.

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