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1. Based on the Central Limit Theorem, the smaller the sample size, the ( larger / smaller ) the standard error of the mean

2. A researcher defines her population of interest as "all high school students who are at risk of dropping out before earning a high school diploma or its equivalent." For that population, an academic achievement test has a mean of 30 and a standard deviation of 6.25. The researcher - having way too much time on her hands - repeatedly selects random samples of ten students from this population. For each sample, she administers the achievement test and calculates the mean score.

a. What is the mean of the sampling distribution created by the researcher?

b. What is the standard error of the mean?

c. Based on this information, is there a high or low likelihood that a sample of ten students exposed to an academic retention program would perform better on the achievement test as a result of the treatment if they had an average score of 35 after treatment? Explain/show why or why not. (Find the z-score and include the proportion/percentage of sample means that are at or above an average of 35)

3. For many years, the average final grade for students taking an introductory stats course has been 76, with a standard deviation of 9. Professor Jones proposes that a weekly tutoring program would improve student performance.

a. State the Hypotheses

b. Establish the critical value if a=.05, and draw a normal distribution with the critical region shaded in A random sample of 30 students from all the sections of introductory stats are tutored throughout the spring semester. Their overall final average is calculated to be 78.

c. Calculate the statistic

d. Make a decision (compare the obtained statistic to the critical value, make a decision, and interpret the statistical results)