Question

In a 2003 article, Hui and Bell (Health and Place. 9:371-376) reported that among 2,428 boys aged 7 to 12 years, 461 were overweight or obese.
a. On the basis of that study, can we conclude that more than 15 percent of the boys aged 7 to 12 in the sampled population are overweight?
b. What is the p-value?
c. What was the null hypothesis?

Answer 1

Answer on Question #44254 – Math - Statistics and Probability

In a 2003 article, Hui and Bell (Health and Place. 9:371-376) reported that among 2,428 boys aged 7 to 12 years, 461 were overweight or obese.

Solution

a. On the basis of that study, can we conclude that more than 15 percent of the boys aged 7 to 12 in the sampled population are overweight?

We can conclude that more than 15 percent of the boys aged 7 to 12 in the sampled population are overweight (the population proportion $p$ is greater than 0.15), so the null hypothesis would be rejected for any reasonable significance level ($\alpha > p$ value = $1.8 \cdot 10^{-8}$).

b. What is the p-value?

$$\hat{p} = \frac{461}{2428} = 0.1899.$$

The value of the test statistic is

$$z = \frac{0.1899 - 0.15}{\sqrt{\frac{0.15 \cdot 0.85}{2428}}} = 5.5061.$$

The p value of this test is

$$p \text{ value} = P(Z > z) = P(Z > 5.5061) = 1.8 \cdot 10^{-8}.$$

c. What was the null hypothesis?

The null hypothesis states that the population proportion of overweight or obese boys of ages 7 to 12 is $\leq 0.15$,

$$H_0: p \leq 0.15.$$

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