Question

It+is+said+60%+of+families+own+a+pet. +of+a+sample+of+95+families,+70+owned+pets. +perform+a+hypothesis+test+to+determine+whether+the+percent+of+families+who+own+pets+is+different+than+60%

Answer 1

There is sufficient evidence to conclude that, the percentage of the families who own a pet is different than 60%.

What are null hypotheses and alternative hypotheses?

In null hypotheses, there is no relationship between the two phenomena under the assumption that it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.

It Is said That 60% of families own a pet.

Of a sample of 95 families, 70 owned pets.

Whether the percent of families who own pets is different than 60%.

Let P be a proportion of the family who owns pets

Then by the test, we have

H₀: P = 0.60

Hₐ: P ≠ 60

Then by the test statistic, we have

$z_o = \dfrac{\bar{P} - P_o}{\sqrt{\dfrac{P_o(1 - P_o)}{n}}}$

Where

$\bar P$  = sample proportion

P₀ = hypothesis proporion

n = sample size

Then we have

$\bar P$ = x/n

$\bar P$ = 70/95

$\bar P$ = 0.74

Then the test statistic will be

$z_o = \dfrac{0.74-0.60}{\sqrt{\dfrac{0.60(1-0.60)}{95}}}$

z₀ = 2.785

Then the critical region will be

Critical value = ± $z_{\alpha /2}$

α = 0.05

α/2 = 0.025

Then we have

z₀.₀₂₅ = 1.96

Then the critical value will be

Critical value = ± 1.96

We reject if $|z_o| > |z_{\alpha /2}|$

We have

$|z_o| > |z_{\alpha /2}|$

2.79 > 1.96

We reject the null hypothesis at a 5% significance level.

There is sufficient evidence to conclude that, the percentage of the families who own a pet is different than 60%.

More about the null hypotheses and alternative hypotheses link is given below.

brainly.com/question/9504281

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