A particular paperback book is published in a choice of four

A particular paperback book is published in a choice of four different covers. A certain bookstore keeps copies of each cover on its racks. To test the hypothesis that sales are equally divided among the four choices, a random sample of 100 purchases is identified.

(a) If the resulting X² value were 6.8, what conclusion would you reach when using a test with significance level .05?

Reject H₀Fail to reject H₀    

(b) What conclusion would be appropriate at significance level .01 if X² = 13.4?

Reject H₀Fail to reject H₀    

(c) If there were six different covers rather than just four, what would you conclude if X² = 12.1 and a test with = .05 was used?

Reject H₀Fail to reject H₀   

Solution

DF = 100-1=99

a)

alpha / 2 = 0.025

critical value : 129.561

X^2 = 6.8

we fail to reject Ho

b)

alpha /2 = 0.005

df = 99

critical value : 140.170

we fail to reject Ho

c)

alpha = 0.05

df = 6-1= 5

critical value : 11.070

we reject Ho because X^2 is gretaer than 11.0701