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There is sufficient evidence to conclude that, the percentage of the families who own a pet is different than 60%.
<h3>What are null hypotheses and alternative hypotheses?</h3>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
Where
= sample proportion
P₀ = hypothesis proporion
n = sample size
Then we have
= x/n
= 70/95
= 0.74
Then the test statistic will be
z₀ = 2.785
Then the critical region will be
Critical value = ±
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
We have
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.
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