If the alpha level is changed from σ= .05 to σ=.01.
a. What happens to the boundaries for the critical region?
b. What happens to the probability of a Type 1error?
Childhood participation in sports, cultural groups, and youth groups appears to be related to improved self-esteem for adolescents (McGee, Williams, Howden Chapman, Martin, & Kawachi, 2006). In a representative study, a sample of n= 100 adolescents with a history of group participation is given in standardized self-esteem questionnaire. For the general population of adolescents, scores on this questionnaire form a normal distribution with a mean of µ= 40 and a stand deviation of σ=12. The sample of group- participation adolescents has an average of M=43.84.
A. Does this sample provide enough evidence to conclude that self-esteem scores these adolescents are significantly different from those of the general population? Use a two tail test with σ= .01
B. Compute Cohen's d to measure the size of the difference.
C. Write a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear in a research report.
A random sample is selected from a normal population with a mean of µ= 50 and a standard deviation of =12. After a treatment is administered to the individual in the sample, the sample mean is found to be M= 55.
A. If the sample consists of n=16 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two tailed test with σ= .05
b. If the sample consists of n=36 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two- tailed test with σ= .05.
c. Comparing your answers for parts a and b, explain how the size of the sample influences the outcome of a hypothesis test.