This question is worth 4 points (most of the other questions are worth 1 point). To receive credit for this question, please ensure that you submit your calculations AND t distribution sketch in the "Calculations Exam 3" document. Ensure that your calculations document includes the following:
All the formulas that you used
Determination of the critical value for this test with alpha = 0.01, including the degrees of freedom you used.
Calculation of the standard error.
Computation of the statistic for the sample mean.
Your t-distribution sketch!
A researcher believes that participating in extracurricular sports during childhood is associated with heightened self-esteem in adolescence. The researcher is aware that, for the overall population of adolescents, scores on a validated self-esteem questionnaire have a mean of mu = 20. To test their hypothesis, the researcher gathers a sample of 25 adolescents who participated in extracurricular sports during childhood. They request these participants to complete the self-esteem questionnaire, yielding an average score of M = 22, a sum of squares ss = 72, and a standard deviation of s = 3. Use the appropriate test with alpha = 0.01 to determine whether adolescents who participated in extracurricular sports during childhood have higher self-esteem compared to the general population. Based on the computed sample statistics, make a decision regarding whether to reject or fail to reject the null hypothesis in this situation.
Question 9 options:
We should reject the alternative hypothesis.
We should not reject the null hypothesis.
We should not reject the alternative hypothesis.
We should reject the null hypothesis.