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

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dfbustos dfbustos · Answer 1 · 2020-05-06T05:03:29+02:00

Answer:

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

Step-by-step explanation:

Data given

n=300 represent the random sample size

[tex]\hat p=0.45[/tex] estimated proportion of people with cats

[tex]p_o=0.40[/tex] is the value that we want to test

[tex]\alpha=0.025[/tex] represent the significance level

z would represent the statistic

[tex]p_v[/tex] 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:[tex]p\leq 0.4[/tex]

Alternative hypothesis:[tex]p > 0.4[/tex]

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:

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

Replacing we got:

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