Exam 6: Hypothesis Tests With Means of Samples

The number of people polled (e.g., in a Gallup poll of U.S. citizens)is not very important; rather, what matters are the methods of sampling and estimating error, which are typically not reported in detail. (True or false)

Place the steps for figuring the 95% and 99% confidence intervals into the correct order. 1. Find the Z scores that go with the confidence interval you want. 2) Change these Z scores to raw scores to find the confidence interval. 3) Estimate the population mean and figure the standard deviation of the distribution of means.

The variance of a distribution of means is the variance of the population of individuals:

A(n)__________ is an estimate of a specific value of a population parameter.

The square root of the variance of the distribution of means is:

The shape of the distribution of means is typically bimodal and symmetrical. (True or False)

For the following question(s): A researcher interested in relationships developed a questionnaire that measures the degree of affection adult men feel for their fathers. She has found that for the general population the distribution is skewed to the right, the mean degree of affection is 60, and the standard deviation is 16. The researcher now is wondering if men who themselves have just become new fathers will score higher on the scale than men in general. She samples a group of 100 new fathers and finds that their mean is 64.5. 26 What is the research hypothesis? A)There will be no significant differences between the two populations. B)The population of new fathers has a higher mean than the mean of the population of men in general. C)The sample size will significantly affect the level of affection experienced. D)The two populations (of men in general and of new fathers)have different variances. Answer: B -What is the standard deviation of the comparison distribution?

The ____________ is the hypothesis-testing procedure used when there is more than one individual in the study's sample and the population variance is known.

In principle, you could make a distribution of means by:

The shape of the distribution of means is approximately normal if either (a)each sample consists of 20 or more individuals or (b)the distributions of the populations of individuals is skewed to the left. (True or False)

Sampling error is usually figured in a large poll:

The distribution of means is the correct comparison distribution when:

Why will you rarely see a Z test in a research article?

All of the following types of distributions are important for hypothesis testing EXCEPT:

Research articles rarely report the standard error (or standard error of the mean)as error bars on graphs. (True or False)

For the following question(s): A population is normally distributed with a mean of 50 and a standard deviation of 8. A sample of 10 is studied. -The mean of the distribution of means = __________.

A private school promoted itself by advertising that its graduates had an average SAT verbal score of 550 (with a standard deviation of 100). At the end of the school year the Parent-Teacher Association (PTA)decided to test this contention and obtained the SAT verbal scores for 80 graduating seniors. Their average score was 532. What should the PTA conclude in regard to the school's claim if a .05 level of significance is used? a. Use the five steps of hypothesis testing. b. Sketch the distributions involved. c. Figure the confidence limits for the 95% confidence interval.

A professor was curious as to whether the students in a very large class she was teaching who turned in their tests first scored differently from the overall mean on the test. The overall mean score on the test was 75 with a standard deviation of 10; the scores were approximately normally distributed. The mean score for the first 20 tests was 78. Did the students turning in their tests first score significantly different from the mean at the .05 level? a. Use the five steps of hypothesis testing. b. Sketch the distributions involved. c. Figure the confidence limits for the 95% confidence interval. d. Explain the logic of what you did to a person who understands hypothesis testing for studies in which the sample consists of a single individual but is unfamiliar with hypothesis testing involving a sample of more than one individual. (Be sure your explanation includes a discussion of the distribution of means-what it is, the logic of how it is figured, and its role in the overall hypothesis-testing process-and the logic and computation of confidence intervals.)

A distribution of means tends to be unimodal and symmetrical because middle scores for means are more likely than extremes, and with fewer extremes there is also less asymmetry. (True or False)

For the following question(s): A researcher interested in relationships developed a questionnaire that measures the degree of affection adult men feel for their fathers. She has found that for the general population the distribution is skewed to the right, the mean degree of affection is 60, and the standard deviation is 16. The researcher now is wondering if men who themselves have just become new fathers will score higher on the scale than men in general. She samples a group of 100 new fathers and finds that their mean is 64.5. 26 What is the research hypothesis? A)There will be no significant differences between the two populations. B)The population of new fathers has a higher mean than the mean of the population of men in general. C)The sample size will significantly affect the level of affection experienced. D)The two populations (of men in general and of new fathers)have different variances. Answer: B -What is the mean of the comparison distribution?