Question

A researcher claims that based on the information obtained from the Centers for Disease Control and Prevention, 23% of young people ages 2-19 are obese. To test this claim, she randomly selected 300 people ages 2-19 and found that 91 were obese. At = 0.01, is there enough evidence to reject the claim?

Answer 1

Here, we have to use one sample z test for the population proportion.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: About 23% of young people ages 2-19 are obese.

Alternative hypothesis: Ha: Other than 23% of young people ages 2-19 are obese.

H0: p = 0.23 versus Ha: p ≠ 0.23

This is a two tailed test.

We are given

Level of significance = α = 0.01

Test statistic formula for this test is given as below:

Z = (p̂ - p)/sqrt(pq/n)

Where, p̂ = Sample proportion, p is population proportion, q = 1 - p, and n is sample size

x = number of items of interest = 91

n = sample size = 300

p̂ = x/n = 91/300 = 0.303333333

p = 0.23

q = 1 - p = 0.77

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.303333333 - 0.23)/sqrt(0.23*0.77/300)

Z = 3.0182

Test statistic = 3.0182

P-value = 0.0025

(by using z-table)

P-value < α = 0.01

So, we reject the null hypothesis

There is not sufficient evidence to conclude that about 23% of young people ages 2-19 are obese.

There is enough evidence to reject the claim.