Question

Think before you post! According to a recent report, 20% of teens aged 13 to 19 say that they have electronically sent or posted suggestive images of themselves. 13 The counselor at a large high school worries that the actual figure might be higher at her school. To find out, she administers an anonymous survey to a random sample of 250 of the school's students. All 250 respond, and 63 admit to sending or posting suggestive images. Do the data give con- vincing evidence at the alpha = 0.05 significance level that the counselor's belief is correct?

Answer 1

Explanation:

To determine if the data give convincing evidence at the alpha = 0.05 significance level that the counselor's belief is correct, we can conduct a hypothesis test.

The null hypothesis is that the proportion of students at the school who have sent or posted suggestive images is equal to 20%, which is the national figure.

The alternate hypothesis is that the proportion of students at the school who have sent or posted suggestive images is greater than 20%

Using a one-sample proportion test and assuming the conditions are met, we can calculate the test statistic and p-value. The p-value can then be compared to the significance level (alpha) to determine if the results are statistically significant. If the p-value is less than the significance level, we can reject the null hypothesis and conclude that the counselor's belief is correct.

Otherwise, we fail to reject the null hypothesis and we cannot conclude that the counselor's belief is correct.