Statistics Ch. 10.3

Question

Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .10 significance level.

The null and alternative hypothesis would be:

H0: PM=PF

H1: PM<PF

The test is: Left tailed

Based on a sample of 40 men, 45% owned cats

Based on a sample of 40 women, 70% owned cats

The test statistic is:________

The p-value is: _______

Based on this we: Reject the null hypothesis

Answer 1

For the first sample,

n1=40, x1=45% of 40=0.45*40=18 men

For the second sample,

n2=40, x2=70 % of 40=0.70*40=28 women

First method, using formula

The test statistics is z value for two sample proportion.

Here, p0=(x1+x2)/(n1+n2)=(18+28)/(40+40)=46/80=0.575

p1 hat=0.45, p2hat=0.70

Plug in the z formula to get the z value=-2.26

The p value from the z table corresponding to z score -2.26=0.0119.

Since the p value is smaller than the significance level of0.10, the null hypothesis is rejected .

Second method, using graphing calculator:

pull up 2-prop z test.

select "less than' option for the alternative hypothesis

plug in x1,n1,x2,n2, significance level 0.10, and run the test to get the above z test statistic and p value.