A study of cats and dogs found that 11 of 50 cats and 21 of

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 ? = .01 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?

Find the null and alternative hypothesis, the z -value, the p-value, and make a decision whether to reject H₀ or not to reject H₀ and write a valid conclusion based on the claim or the test.

Solution

p1=11/50 =0.22

p2= 21/50 = 0.42

Null hypothesis: p1=p2

Alternative hypothesis: p1 not equal to p2

The test statistic is

Z=(p1-p2)/sqrt(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

It is a two-tailed test.

So the p-value= 2*P(Z<-2.19) = 0.0285 (from standard normal table)

Since the p-value is larger than 0.01, we do not reject Ho.

So we can not conclude that a difference exists between the proportion of cats and the proportion of dogs that sleep more than 10 hours per day