Question

Teens and sex The Gallup Youth Survey asked a random sample of U.S. teens aged 13 to 17 whether they thought that young people should wait to have sex until marriage.17 The Minitab output below shows the results of a significance test and a 95% confidence interval based on the survey data.

(a) Define the parameter of interest.

(b) Check that the conditions for performing the significance test are met in this case.

(c) Interpret the P-value in context.

(d) Do these data give convincing evidence that the actual population proportion differs from 0.5? Justify your answer with appropriate evidence.

Short answer

Part (a) Population Proportion

Part (b) Significant if the p-value is less than 0.05.

Part (c) 0.011<0.05

Part (d) Yes, the actual population differs from 0.5.

Step-by-step solution

Part (a)  Step 1. Parameter of Interest 

The Minitab output represents the confidence interval of the population proportion. So, the parameter of interest is the population proportion.

Part (b) Step 1. Decision Criteria 

The criteria for testing whether the hypothesis test is significant or not. In other words, if the probability of rejecting the null hypothesis is less than 0.05 implies that the test is significant.

Part (c) Step 1. Interpretation 

It can be observed that the p-value is less than 0.05, that is,

$0.011<0.05$

As a result, the test is significant as there is enough evidence to reject the null hypothesis.

Part (d) Step 1. Significance of the test

It can be observed that there is enough evidence to reject the null hypothesis and the test is significant. So, the alternate hypothesis is accepted, and the actual population differs from 0.5.