Problem Set 1: Chapter 8, problems 2, 4, 6, 10, 12, 22, 24
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:
4. If the alpha level is changed from a = .05 to a = .01,
a. What happens to the boundaries for the critical regions?
b. What happens to the probability of a type I error?
6. A researcher is investigating the effectiveness of a new study-skills training program for elementary school children. A sample of n= 25 third grade children and each child is given a standardized achievement test at the end of the year. For the regular population of third grade children, scores on the test form a normal distribution with a mean of u = 150 and a standard deviation of o= 25. The mean for the sample is M = 158.
a. Identity the independent and the dependent variables for this study.
b. Assuming two-tailed test, state the hypotheses (Ho and H1 ) for the two-tailed test.
c. Using symbols, state the hypotheses (Ho and H1) for the two-tailed test.
d. Sketch the appropriate distribution, and locate the critical regions for a= .05.
e. Calculate the test statistics (z score) for the sample.
f. What decision should be made about the effect of the program?
10. State College is evaluating a new English composition course for freshmen. A random sample of n = 25 freshmen is obtained and the students are placed in the course during their first semester. One year later, a writing sample is obtained for each student and the writing samples are graded using a standardized evaluation technique. The average score for the sample is M = 76. For the general population of college students, writing scores form a normal distribution with a mean of u = 70.
a. If the writing scores for the population have a standard deviation of o = 20, does the sample provide enough evidence to conclude that the new composition course has a significant effect?
b. If the population standard deviation is o = 10, is the sample sufficient to demonstrate a significant effect? Again, assume a two-tailed test with a= .05.
c. Briefly explain why you reached different conclusions for part (a) and part (b).
12. To test the effectiveness of a treatment, a sample of n = 25 people is selected from a normal population with a mean of u = 60. After the treatment is administered to the individuals in the sample, the sample mean is found to be M = 55.
a. If the population standard deviation is o = 10, can you conclude that the treatment has a significant effect? Use a two-tailed with a = .05.
b. If the population standard deviation is o = 20, can you conclude that the treatment has s significant effect? Use a two-tailed test with a= .05.
c. Compute Cohen's d measure effect size for both tests (n= 4 and n = 36).
d. Briefly describe how sample size influence the outcome of the hypothesis test. How does sample size influence measures of effect size?
22. Explain how the power of a hypothesis test is influenced by each of the following. Assume that all other factors are held constant.
a. Increasing the alpha level from .01 to .05.
b. Changing from a one-tailed test to a two-tailed test.
24. A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of u = 80 and a standard deviation of o= 20. The researcher expects a 12 point treatment effect and plans to use a two-tailed hypothesis test with u a = .05
a. Compute the power of the test if the researcher uses a sample of n = 16 individuals.
b. Compute the power of the test if the researcher uses a sample of n = 25 individuals.
Explains in detail several of the concepts underlying z tests, hypothesis testing, statistical decisions, power, Type I errors, and effect size. Shows calculations and graphs. Step-by-step solution of several classic problems.