Question

A researcher claims that based on the information obtained from the Centers for Disease Control and Prevention, 17% of young people ages 2-19 are obese. To test this claim, she randomly selected 200 people ages 2-19 and found that 42 were obese. At alpha = 0:05, is there enough evidence to reject the claim?

State the null and alternative hypotheses.

Answer 1

To determine if there's enough evidence to reject the researcher's claim that 17% of young people ages 2-19 are obese, we would state the null hypothesis as the population proportion being equal to 0.17, and the alternative hypothesis as the population proportion not being equal to 0.17. Then, we conduct a hypothesis test using the sample data.

Step-by-step explanation:

The researcher's claim that 17% of young people ages 2-19 are obese is being tested with a sample of 200 people, out of which 42 were found to be obese. To conduct a hypothesis test at the alpha level of 0.05, we need to state the null and alternative hypotheses.

The null hypothesis (H0) for this test would be that the true proportion of obesity in the population is equal to the claimed proportion, which is:
H0: p = 0.17

The alternative hypothesis (Ha) would be that the true proportion of obesity is different from the claimed proportion:
Ha: p ≠ 0.17

We would then perform the hypothesis test to see if the observed sample proportion (which is 42/200 = 0.21) significantly differs from the claimed proportion of 0.17. If the p-value is less than alpha (0.05), we would reject the null hypothesis, indicating there is enough evidence to suggest that the true proportion is different from 17%.