Question

Does participation in sports, cultural groups, and youth groups improve self esteem for adolescents? What do you think? A study done by McGee et al. (2006) claims that involvement in these groups does improve self-esteem.

Following the steps for statistical hypothesis testing, you embark on an independent investigation.

For your study, you have randomly selected 100 adolescents with a history of group participation and give them a standardized self-esteem questionnaire. The sample of group-participation adolescents scored a mean of 46.1 on the questionnaire. You also know that for the general population of adolescents, scores on this questionnaire form a normal distribution with a population mean (μ) of 41.7 and a population standard deviation (σx) of 18.2

7) Elaborate on what this test allows us to conclude about how participation in sports, cultural groups, and youth groups affects self-esteem for adolescents. In other words, interpret your results. What does the data tell us about our research question?

8) Now suppose instead of a two-tailed test you are interested in a one-tailed test (After all you were only interested in whether participation would improve self-esteem). Draw a sampling distribution for a one-tailed test using the standard .05 level for alpha. Again, in your drawing mark your critical value (Zcrit), your rejection region, and your obtained value (Zobt).

9) Again, compare your Zobt to your Zcrit and interpret your Zobt. Is your conclusion the same or different than it was for the two-tailed test?

10) Despite our best attempts in using the logic of probability to make the appropriate inferences from a sample, we run the risk of committing errors. In your own words, describe what the two types of errors are, then indicate what type of errors you are at risk of committing in (6) and in (9) based on your statistical decision?

Answer 1

7) We will conduct a Z test for the population mean as the standard deviation of the population is mentioned.This test allows us to conclude that participation in sports, cultural groups, and youth groups increases the self-esteem for adolescents.

8-9)

The conclusion is same for rejection of the null hypothesis.

10) two type of errors can occur

1) a type I error is the rejection of a true null hypothesis (also known as a "false positive" finding), 2)  type II error is failing to reject a false null hypothesis (also known as a "false negative" finding).