Question

Test the claim that the proportion of people who own cats is larger than 40% at the 0.025 significance level. The null and alternative hypothesis would be: H 0 : p = 0.4 H a : p ≠ 0.4 H 0 : μ ≥ 0.4 H a : μ < 0.4 H 0 : μ ≤ 0.4 H a : μ > 0.4 H 0 : μ = 0.4 H a : μ ≠ 0.4 H 0 : p ≤ 0.4 H a : p > 0.4 H 0 : p ≥ 0.4 H a : p < 0.4 The test is: right-tailed left-tailed two-tailed Based on a sample of 300 people, 45% owned cats

Answer 1

H 0 : p ≤ 0.4 H a : p > 0.4

And based on the alternative hypothesis we can conclude that we have a right tailed test

Explanation:

Data given

n=300 represent the random sample size

`\hat p=0.45` estimated proportion of people with cats

`p_o=0.40` is the value that we want to test

`\alpha=0.025` represent the significance level

z would represent the statistic

`p_v` represent the p value

Null and alternative hypothesis

We want to test if the true proportion of people with cats is higher than 0.4, so then the best alternative is:

Null hypothesis:
`p\leq 0.4`

Alternative hypothesis:
`p > 0.4`

H 0 : p ≤ 0.4 H a : p > 0.4

And based on the alternative hypothesis we can conclude that we have a right tailed test

The statistic is given by:

`z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}}` (1)

Replacing we got:

`z=\frac{0.45 -0.4}{\sqrt{(0.4(1-0.4))/(300)}}=1.768`