Deck 6: Hypothesis Tests With Means of Samples

Question 1

As the number of individuals in each sample gets larger, the distribution of means:

A)begins to look less and less like the normal curve (in terms of shape)
B)becomes a better approximation of the normal curve (in terms of shape)
C)becomes more positively skewed
D)becomes more negatively skewed

Answer 1

becomes a better approximation of the normal curve (in terms of shape)

Question 2

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

A)figuring the mean of all the possible samples of a given size and dividing it by the variance
B)using the sample's mean and variance divided by the population's parameters
C)randomly estimating the population variance from the various samples of the same size, and using the sample mean in place of the population mean
D)randomly taking a very large number of samples from a population, each of the same size, and making a distribution of their means

Answer 2

randomly taking a very large number of samples from a population, each of the same size, and making a distribution of their means

Question 3

When a researcher has obtained a particular sample mean from a study, he or she compares it to:

A)the parameters of the known population distribution
B)an estimated distribution figured based on earlier research findings
C)the distribution of means of all the possible samples in the experimental condition from the research
D)the distribution of means that would arise if the null hypothesis were true

Answer 3

the distribution of means that would arise if the null hypothesis were true

Question 4

The standard deviation of a distribution of means is:

A)figured by subtracting the variance from the sample mean and then taking the square root
B)the square root of the variance of the distribution of means
C)the population variance divided by the number of individuals in each sample
D)the same as the square root of the sample variance

Question 5

For a particular known population, the mean is 100 and the variance is 25. A researcher conducts a study in which 10 participants are exposed to an experimental procedure. To test the hypothesis that the population these 10 participants represent is different from the known population, the comparison distribution's mean and variance would be:

A)mean = 10, variance = 2.5
B)mean = 10, variance = 5
C)mean = 100, variance = 2.5
D)mean = 100, variance = 5

Question 6

The standard deviation of the distribution of means is also known as the:

A)population standard deviation
B)variance of the error mean
C)standard error of the population
D)standard error of the mean

Question 7

The distribution of means is also called:

A)distribution of samples of means
B)standard deviation of the mean
C)sampling distribution of the mean
D)sampling distribution of the mode

Question 8

The distribution of means is the correct comparison distribution when:

A)there is more than one person in a sample
B)there is less than one person in a sample
C)the mean is greater than the median in your sample
D)the mode is equal to the mean and median in your sample

Question 9

A distribution of means will be less spread out than the population of individuals from which the samples are taken because:

A)in a sample of scores, extremes tend to be balanced out, leaving fewer extreme means
B)in a sample of scores, there tend to be multiple extreme means
C)each sample is based on randomly selected individuals from the population
D)the more individuals in each sample, the more spread out will be the sample means

Question 10

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

A)multiplied by the number of individuals in each sample
B)divided by the number of individuals in each sample
C)squared
D)divided by the mean of the population

Question 11

The variance of a distribution of means of samples of more than one is:

A)smaller than the original population variance
B)the same as the original population variance
C)greater than the original population variance
D)unrelated to the original population variance

Question 12

Knowledge of what three important characteristics of the comparison distribution is required for hypothesis testing?

A)the median, mean, and variance
B)the mean, median, and mode
C)the mean, spread, and shape
D)the mean, standard deviation, and size

Question 13

The variance of a distribution of means is less than the original population variance because:

A)it is based on fewer individuals than of the original population
B)it is an estimate of the sample parameters rather than the original population
C)extreme scores are less likely to affect a distribution of means
D)a distribution of means actually has a larger variance than the original population

Question 14

In general, the shape of a distribution of means tends to be:

A)unimodal, symmetrical
B)bimodal, symmetrical
C)unimodal, skewed
D)rectangular, symmetrical

Question 15

The proper comparison distribution for the mean of a sample is called the distribution of means and is used because:

A)comparing the mean of a sample to a population distribution of individual scores is a mismatch
B)the available population parameters are inaccurate and reflect too little variance within the population
C)the distribution of means is likely to have more varied scores than would be represented in the population
D)the proper comparison distribution is stated in the null hypothesis

Question 16

A distribution of means is a distribution of the means of each of many samples __________.

A)of varying size and shape
B)of equal size
C)randomly taken from the same population of individuals
D)both B and C

Question 17

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

A)the estimated sample variance
B)the average deviation of the original population
C)an unbiased estimate of the population standard deviation
D)the standard deviation of the distribution of means

Question 18

Dividing the variance of the population of individuals by the number of individuals in each sample gives:

A)the standard deviation of the population
B)the variance of the distribution of means
C)an estimate of the sample's standard deviation
D)the average deviation of the distribution of means

Question 19

With samples of 30 or more individuals, the approximation of the distribution of means will be:

A)a bimodal distribution
B)a rectangular distribution
C)a normal curve
D)the distribution of Z scores

Question 20

The mean of a distribution of means is:

A)the square root of the original population mean
B)the original population mean divided by the sample size
C)the same as the original population mean
D)the sample mean multiplied by the variance

Question 21

For the following question(s): A researcher is interested in whether the color of an animal's surroundings affects learning rate. She tests 16 rats in a box with colorful wallpaper. Assume that it is known that the average rat can learn to run this particular maze (in a box without any special coloring)in 25 trials, with a variance of 64; the distribution is normal. The mean number of trials to learn the maze for the group with the colorful wallpaper is 11.
What is the standard deviation of the distribution of means?

A)64/16 = 4.00
B)square root of (64/16)= 2.00
C)64/11 = 5.82
D)square root of (64/11)= 2.41

Question 22

How do you find the Z score for a sample's mean on the distribution of means?

A)Use the standard formula for changing a raw score to a Z score.
B)Use the standard formula for changing a raw score to a Z score, using the mean and median of the distribution of means.
C)Use the standard formula for changing a raw score to a Z score, using the mean and standard deviation of the distribution of means.
D)Use the standard formula for converting a raw score to a Z score but use the T distribution.

Question 23

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.

A)Z test
B)F test
C)T test
D)K test

Question 24

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

A)the distribution of a population of individuals
B)the distribution of a particular sample of individuals taken from the population
C)the distribution of R scores
D)the distribution of means

Question 25

The difference between creating a Z score from a single score and creating one from a sample mean is that:

A)you use the mean and standard deviation from the distribution of means
B)the estimated population variance is used directly
C)the difference score is divided by the sample's standard deviation
D)only the population's mean is used

Question 26

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 variance on this questionnaire in the general population?

A)16
B)320
C)256
D)500

Question 27

For a 99% confidence interval, you use the Z scores for the middle 99% of the normal curve, which comes out to:

A)+1.64 and -1.64
B)+2.58 and -2.58
C)+3.04 and -3.04
D)+1.58 and -1.58

Question 28

For the following question(s): A researcher is interested in whether the color of an animal's surroundings affects learning rate. She tests 16 rats in a box with colorful wallpaper. Assume that it is known that the average rat can learn to run this particular maze (in a box without any special coloring)in 25 trials, with a variance of 64; the distribution is normal. The mean number of trials to learn the maze for the group with the colorful wallpaper is 11.
What is the shape of the distribution of means?

A)rectangular
B)normal
C)not rectangular, but flatter than a normal curve
D)it cannot be determined from the information given

Question 29

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

A)Research in which there is a known population mean and standard deviation is rare in behavioral and social science research.
B)Research in which there is a known sample mean and mode is rare in behavioral and social science research.
C)These articles tend not to be favored by journal reviewers.
D)It is not the case that you will rarely see a Z test in a research article.

Question 30

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?

A)60/100 = .60
B)60
C)64.5/100 = .645
D)64.5

Question 31

A region of scores estimated to include a population parameter such as the population mean is called:

A)a point estimate
B)an interval estimate
C)a confidence interval
D)both B and C

Question 32

A 99% confidence interval is the region:

A)that you are 99% confident includes the true population mean
B)that you are 1% confident includes the true population mean
C)that includes 49% of the scores below the point estimate of the mean and 50% of the scores above the point estimate of the mean
D)that includes 50% of the scores below the point estimate of the mean and 49% of the scores above the point estimate of the mean

Question 33

The best estimate of the population mean is the:

A)population median
B)sample mode
C)sample median
D)sample mean

Question 34

For the following question(s): A researcher is interested in whether the color of an animal's surroundings affects learning rate. She tests 16 rats in a box with colorful wallpaper. Assume that it is known that the average rat can learn to run this particular maze (in a box without any special coloring)in 25 trials, with a variance of 64; the distribution is normal. The mean number of trials to learn the maze for the group with the colorful wallpaper is 11.
What is the null hypothesis?

A)The rate of learning for the sample of rats tested with colorful wallpaper is no different than the population of rats tested under ordinary circumstances.
B)The rate of learning for the sample of rats tested with colorful wallpaper is faster than the population of rats tested under ordinary circumstances.
C)The rate of learning for the population of rats tested with colorful wallpaper is no different than the population of rats tested under ordinary circumstances.
D)The rate of learning for the population of rats tested with colorful wallpaper is faster than the population of rats tested under ordinary circumstances.

Question 35

The 95% confidence interval:

A)will be narrower than the 99% confidence interval
B)will be wider than the 99% confidence interval
C)will have the same upper limit as the 99% confidence interval but a different lower limit
D)will have the same lower limit as the 99% confidence interval but a different upper limit

Question 36

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?

A)16/100 = .16
B)square root of 16/100 = .40
C)162/100 = 16.2
D)square root of (16*16)/100 = 1.6

Question 37

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 shape of the comparison distribution?

A)approximately normal
B)skewed to the left
C)skewed to the right
D)it cannot be determined from the information given

Question 38

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)

Question 39

Suppose the sample mean's score on the comparison distribution is more extreme than the cutoff. What would the researcher conclude regarding the colorful wallpaper?

A)She should reject the null hypothesis that the rats in the sample will learn faster.
B)The wallpaper did not have a significant effect on the rate of learning.
C)The color of the chamber had a significant effect on the rate of learning.
D)The results are inconclusive since the null hypothesis cannot be rejected.

Question 40

The Z score of the sample mean on the distribution of means is:

A)different from a normal Z score because an estimated population standard deviation is used
B)smaller than normal due to the reduced variance in the distribution of means
C)conceptually similar to creating a Z score from a raw score
D)equivalent to the sample mean divided by the population variance

Question 41

A researcher explained that the average amount of hours studied by students per week in a particular statistics course was 3.6 with a 95% confidence interval of 2.40-4.8. This would tell you that the true amount of study time is probably between:

A)2)4 and 3.6
B)3)6 and 4.8
C)2)4 and 4.8
D)0 and 1

Question 42

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)

Question 43

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)

Question 44

The __________ of a distribution of means equals the __________ of the population divided by the number of individuals in the sample. (Use the same word in both places.)

Question 45

When conducting a study involving a sample of several people to see whether they represent a population different from some known population, the __________ is a distribution of means.

Question 46

The mean of a distribution of means is __________ the mean of the population.

Question 47

The variance of a distribution of means equals the variance of the population of individuals divided by the __________.

Question 48

The variance of the distribution of means = __________.

Question 49

In a research article involving a sample and a known population mean, frequently reported statistics would include:

A)the standard error and the mean
B)the power, effect size, and mode
C)t scores, Z scores, and variance
D)t scores and the distribution of means

Question 50

"Population SD²_M" stands for __________.

Question 51

There is no reason for the mean of a distribution of means to be larger or smaller than the __________.

Question 52

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 = __________.

Question 53

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.

A)3, 1, 2
B)2, 1, 3
C)1, 2, 3
D)2, 3, 1

Question 54

A(n)__________ is the comparison distribution when testing a hypothesis involving a sample of more than one individual.

Question 55

The standard deviation of a distribution of means is the square root of the variance of __________.

Question 56

The advantage of a large sample size, like those used in polls, is that they:

A)increase the score needed for a significant result
B)increase the probability of a Type I error
C)greatly reduce the standard deviation of the distribution of means
D)decrease the probability of correctly rejecting the null hypothesis

Question 57

Another name for the standard deviation of a distribution of means is the __________.

Question 58

Other names for the standard error include the standard deviation of the distribution of means and the standard error of the mean. (True or False)

Question 59

The shape of the distribution of means is __________.

Question 60

Sampling error is usually figured in a large poll:

A)by dividing the variance of the distribution of means by the N of each sample
B)by squaring the variance
C)from the proportion of the population that the sample represents
D)from preconstructed tables indexed by the sample size

Question 61

For the 95% confidence interval, the Z scores utilized to form the interval are:

Question 62

Do corporate executives who exercise regularly score lower than corporate executives in general on a scale of stress symptoms? For corporate executives in general, the average on this test is 80 with a standard deviation of 12. The distribution is normal. A researcher measured 20 exercising executives and found them to have a mean score of 72. Is this difference significant at the .05 level?
a. Use the five steps of hypothesis testing.
b. Figure the confidence limits for the 95% confidence interval.
c. Explain the logic of what you did to a person who is unfamiliar with hypothesis testing involving a sample of more than one individual.

Question 63

The standard deviation of __________ is generally referred to as the standard error (SE)in research articles.

Question 64

A school counselor was interested in the effect of a new program designed to reduce adjustment problems in newly transferred students. From her years of working at the school, she knew that the average score on a scale of adjustment difficulties for a transfer student was 58 with a standard deviation of 10. After the new program had been implemented, she tested 50 students and found their mean to be 52. Was this difference significant at the .01 level?
a. Use the five steps of hypothesis testing.
b. Sketch the distributions involved.
c. Figure the confidence limits for the 99% confidence interval.

Question 65

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

Question 66

A school principal was interested in whether students in the chess club scored above or below the mean grade point average (GPA)at her school. She figured the average GPA at the school to be 2.55 with a standard deviation of .5 and noted that the distribution was approximately normal. She then figured the average GPA for 15 students in the chess club. Their mean GPA was 2.76. Did this group represent a population different from students in general at this school? (Use the .05 significance level.)
a. Use the five steps of hypothesis testing.
b. Figure the confidence limits for the 95% confidence interval.
c. Explain the logic of what you did to a person who 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.)

Question 67

The __________ are the upper and lower ends of the confidence interval.

Question 68

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.)

Question 69

The following statements were printed in journal articles in the field of psychology. Explain what each statement means to a person who is unfamiliar with the concept of confidence intervals:
a. "The average grade point average of a Greenwald State College Student is 2.9 ±.3 (95% CI)."
b. "The average number of overtime hours worked in the plumbing industry is 3.7 with a 99% confidence interval of 2.5-4.9."
c. "Each 1 hour per day of brisk walking is associated with a 24% (95% CI, 19-29%)reduction in obesity."

Question 70

In survey work and polls, the absolute number of people polled is not very important, but what maters very much are the methods of sampling and estimating error. (True or False)

Question 71

95% and 99% are common ranges for __________.

Question 72

A researcher can use confidence intervals to do hypothesis testing. If the confidence interval does not include the mean of the null hypothesis distribution, then the result is significant. (True or False)

Question 73

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

Question 74

A(n)__________ is the name of the hypothesis-testing procedure used when there is a single sample and a known population.

Question 75

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.

Question 76

A distribution of means will be approximately normal so long as there are at least __________ individuals in the samples.

Question 77

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