Statistics

Statistics

2. The value of the z-score in a hypothesis test is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of z is influenced by each of the following:

a.Increasing the difference between the sample mean and the original population mean.

z-score = (sample mean - population mean) / (s.d./sqrt(n)

So, if the difference between the sample mean and the original population mean increase, the z-score will increase.

b.Increasing the population standard deviation.

From the definition of z-score, if the standard deviation increase, the z-score will decrease.

c.Increasing the number of scores in the sample

From the definition of z-score, if the number of scores in the sample increase, the z-score will increase.

4. If the alpha level is changed from a=.05 to a= .01,

a. What happens to the boundaries for the critical region?

The boundaries of the critical region will increases.

b. What happens to the probability of a Type I error?

The probability of type I error will decrease.

6) 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 a 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 standard deviation of r =12. The sample of group participation adolescents had an average of M =43.84.

Does this sample provide enough evidence to conclude that self-esteem scores for these adolescents are significantly different from those of the general population? Use a two -tailed test with a=.01.

z score = (M - µ) / (o/(n) = (43.84- 40)/(12/sqrt(100) = 3.2

p-value = 0.0014

Yes, the sample provide enough evidence to conclude that self-esteem scores for these adolescents are significantly different from those of the general population.

Compute Cohen's d to measure the size of the difference.

Cohen's d for test = Mean difference/s.d. = 3.84/12 = 0.32

Write a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear in a research report.

The sample is large enough to support the hypothesis as p < 0.05 and also the Cohen's is showing minimum differences as the sample size changes.

8) A random sample is selected from a normal population with a mean of µ =50 and a standard deviation of ...