Question

1. You are testing the claim that the proportion of men who own cats is larger than the proportion of women who own cats. You sample 70 men, and 30% own cats. You sample 170 women, and 10% own cats. Find the proportion of the pooled samples, (p sub c), as a decimal, rounded to two decimal places.

2. 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. left tailed right tailed two tailed test statistic critical value reject or accept the null

3. A survey of 47 people was conducted to compare their self-reported height to their actual height. The difference between reported height and actual height was calculated.

You're testing the claim that the mean difference is greater than 1.5.

From the sample, the mean difference was 1.8, with a standard deviation of 0.72.

Calculate the test statistic, rounded to two decimal places

Answer 1

1)

P1 = 0.3, N1 = 70

P2 = 0.1, N2 = 170

Pooled proportion = (p1*n1 + p2*n2)/(n1+n2) = 0.15833333333 = 0.16

2)

Null hypothesis Ho : P 1 = P2

Alternate hypothesis Ha : P1 < P2

Left tailed

First we need to check the conditions of normality that is if n1p1 and n1*(1-p1) and n2*p2 and n2*(1-p2) all are greater than equal to 5 or not

N1*p1 = 21

N1*(1-p1) = 49

N2*p2 = 17

N2*(1-p2) = 153

All the conditions are met so we can use standard normal z table to conduct the test

Test statistics z = (P1-P2)/standard error

Standard error = √{p*(1-p)}*√{(1/n1)+(1/n2)}

P = pooled proportion = [(p1*n1)+(p2*n2)]/[n1+n2]

After substitution

Test statistics z = 3.84

From z table, P(Z<3.84) = 1

So, P-Value = 1

As the obtained P-Value is greater than the given significance(0.1)

We fail to reject the null hypothesis Ho