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? Complete the output to include the following steps: 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.

1. 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?
Complete the output to include the following steps: 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