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. a) Find the p-value for the test. b) If you plan to conduct your test using a = 13.2% what will your conclusion be?

Answer 1

The following information is provided: The sample size is N = 200, the number of favorable cases is X = 42, and the sample proportion is p = + = = 0.21, and the significance level is a = 0.1320 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho:p=0.17 Ha:p +0.17 This corresponds to a two-tailed test, for which a z-test for one population proportion needs to be used

Test Statistics

The z-statistic is computed as follows:

р - Po V po 1 - po)/n 0.21 -0.17 0.17(1 - 0.17)/200 1.506

Using the P-value approach: The p-value is p = 0.1321, and since p=0.1321 > 0.1320, it is concluded that the null hypothesis is not rejected.

P value =0.1321

( b )

Conclusion :

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is enough evidence to

claim that  17% of young people ages 2 -9 are obese  at the α=0.1320 significance level.