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# Statistics

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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.

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).