Question

We want to know if whether you read fiction or non-fiction affects whether or not you use e-books or print books. We sample 130 people and ask them whether the last book they read was fiction or non-fiction, and whether or not it was an e-book or a print book. We found that there were 60 had read a non-fiction book in the last year, and of those 60, 40 had read a print book. Of the 70 who had read a fiction book most recently, 35 had read a print book.

What is the conditional distribution for e-book and print books when looking only at those who read fiction?

What is the marginal distribution for e-book and print book reading?

We want to perform a χ₂ test. Give the hypotheses.

Find the expected counts for the table

Find the test statistic for the table. Give its degrees of freedom.

The p-value is .1962. Assuming a significance level of .05, make a decision and write a

conclusion.

Answer 1

Observed Frequencies:

	Fiction	Non-fiction	Marginal Totals
e-book	35=O11	20=O12	55=O10
Print book	35=O21	40=O22	75=O20
Marginal totals	70=O01	60=O02	130=N

The conditional distribution for e-book and print books when looking only at those who read fiction:

P(e-book|Fiction)=O11/O01=35/70=1/2

P(Print book|Fiction) =O21/O01=35/70=1/2

The marginal distribution for e-book and print book reading:

P(e-book)=55/130=11/26, P(Print book)=75/130=15/26.

Null hypothesis, H0: fiction or non-fiction does not affects whether or not you use e-books or print books

vs. Alternative hypothesis, H1: fiction or non-fiction affects whether or not you use e-books or print books

Expected Count:

	Fiction	Non-fiction
E-book	29.6154=e11	25.3846=e12
Print book	40.3846=e21	34.6154=e22

Degrees of freedom=(2-1)(2-1)=1

Hence we fail to reject H0 at 5% level of significance and conclude that you read fiction or non-fiction does not affect whether or not you use e-books or print books.