Statistics

1. 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 is selected to participate in the program and each child si 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 150 and a standard deviation of 25. The mean for the sample is M = 158.

a. Identify the independent and the dependent variables for this study.
b. Assuming a two-tailed test, state the null hypothesis in a sentence that includes the independent variable and the dependent variable.
c. Using symbols, state the hypotheses H0 and H1) for the two-tailed test.
d. Sketch the appropriate distribution, and locate the critical region for alpha = .05.
e. Calculate the test statistic (z-score) for the sample.
f. What decision should be made about the null hypothesis, and what decision should be made about the effect of the program?

2. If the alpha level is changed from alpha = .05 to alpha = .01
a. What happens to the boundaries for the critical region?
b. What happens to the probability of a Type 1 error?

3. 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 = 70.
a. If the writing scores for the population have a standard deviation of 20, does the sample provide enough evidence to conclude that the new composition course has a significant effect? Assume a two-tailed test with alpha = .05.
b. If the population standard deviation is 10, is the sample sufficient to demonstrate a significant effect? Again, assume a two-tailed test with alpha = .05.
c. Briefly explain why you reached different conclusions for part (a) and part (b).