A study of cats and dogs found that 11 of 50 cats and 21 of 50 dogs slept more t

Question

A study of cats and dogs found that 11 of 50 cats and 21 of 50 dogs slept more than 10
hours per day. At the .05 level of significance, is there sufficient evidence to conclude
that a difference exists between the proportion of cats and the proportion of dogs that
sleep more than 10 hours per day?
A) No, there is not sufficient information to reject the hypothesis that the proportion of
cats and the proportion of dogs that sleep more than 10 hours per day are the same
because the test value –0.65 is inside the acceptance region (-1.96,1.96).
B) Yes, there is sufficient information to reject the hypothesis that the proportion of
cats and the proportion of dogs that sleep more than 10 hours per day are the same
because the test value –2.14 is outside the acceptance region (-1.96,1.96).
C) No, there is not sufficient information to reject the hypothesis that the proportion of
cats and the proportion of dogs that sleep more than 10 hours per day are the same
because the test value –1.40 is inside the acceptance region (-1.96,1.96).
D) Yes, there is sufficient information to reject the hypothesis that the proportion of
cats and the proportion of dogs that sleep more than 10 hours per day are the same
because the test value –2.47 is outside the acceptance region (-1.96,1.96).

Explanation / Answer

Given n1=50, p1=11/50=0.22
n2=50, p2=21/50=0.42

The test statistic is
Z=[(p1-p1)-10]/[(p1*(1-p1)/n1) + (p2*(1-p2)/n2)]

=(0.22-0.42)/sqrt(0.22*(1-0.22)/50 + 0.42*(1-0.42)/50)

= -2.19

Answer: B) Yes, there is sufficient information to reject the hypothesis that the proportion of
cats and the proportion of dogs that sleep more than 10 hours per day are the same
because the test value –2.14 is outside the acceptance region (-1.96,1.96).

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