Chapter 6

1. What are the mean and standard deviation of the sampling distribution of the mean?

2. Given a test that is normally distributed with a mean of 30 and a standard deviation of 6,

(a) What is the probability that a single score drawn at random will be greater than 34?

(b) What is the probability that a sample of 9 scores will have a mean greater than 34?

(c) What is the probability that the mean of a sample of 16 scores will be either less than 28 or greater than 32?

3. What is a standard error and why is it important?

4. What is the relationship between sample size and the standard error of the mean?

5. What is the symbol used to designate the standard error of the mean? The standard error of the median?

6. Young children typically do not know that memory for a list of words is better if you rehearse the words. Assume two populations: (1) four-year-old children instructed to rehearse the words and (2) four-year-old children not given any specific instructions. Assume that the mean and standard deviation of the number of words recalled by Population 1 are 3.5 and .8. For Population 2, the mean and standard deviation are 2.4 and 0.9. If both populations are normally distributed, what is the probability that the mean of a sample of 10 from Population 1 will exceed the mean of a sample of 12 from Population 2 by 1.8 or more?

7. Assume four normally-distributed populations with means of 9.8, 11, 12, and 10.4 all with the same standard deviation of 5. Nine subjects are sampled from each population and the mean of each sample computed. What is the probability that average of the means of the samples from Populations 1 and 2 will be greater than the average of the means of the samples from Populations 3 and 4?

8. If the correlation between reading achievement and math achievement in the population of fifth graders were .45, what would be the probability that in a sample of 12 students, the sample correlation coefficient would be greater than .7?

9. If numerous samples of N = 15 are taken from a uniform distribution and a relative frequency distribution of the means drawn, what would be the shape of the frequency distribution?

10. If a fair coin is flipped 18 times, what is the probability it will come up heads 14 or more times?

11. Some computer programs require the user to type in commands to get the program to do what he or she wants. Others allow the user to choose from menus and push buttons. Assume that .45 of office workers are able to solve a particular problem using a program that is "command based" and that .83 of workers can solve the problem using a "menu/button based" program. If two samples of 12 subjects are tested, one with each program, what is the probability that difference in the proportions solving the problem will be greater than .5?