Deck 5: Hypothesis Tests With Means of Samples

Question 1

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 in the computation.

Answer 1

you use the mean and standard deviation from the distribution of means.

Question 2

The mean and variance of a comparison distribution that would be used to test the hypothesis that the mean obtained in a study involving 10 participants is different from a known population having a mean of μ = 100 and σ² = 25 would be

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

Answer 2

mean = 100,variance = 2.5

Question 3

If a population is not normally distributed,the shape of a distribution of means

A)will always be normal.
B)will never be normal.
C)will be normal when the sample size is more than 30.
D)will not be normal when the sample size is more than 30.

Answer 3

will be normal when the sample size is more than 30.

Question 4

An experimental psychologist is interested in whether the color of an animal's surroundings affects learning rate. He tests 16 rats in a box with colorful wallpaper. The average rat (of this strain) can learn to run this type of maze in a box without any special coloring in an average of 25 trials, with a variance of 64, and a normal distribution. The mean number of trials to learn the maze, for the rats tested with the colorful wallpaper, is 11.
The shape of the distribution of means

A)will be rectangular.
B)will be flatter than a normal curve.
C)will be approximately normal.
D)cannot be determined from the information given.

Question 5

When hypothesis testing with a sample of two or more,the formula for figuring your sample's score on the comparison distribution is

A)
B)
C)
D)

Question 6

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 7

An experimental psychologist is interested in whether the color of an animal's surroundings affects learning rate. He tests 16 rats in a box with colorful wallpaper. The average rat (of this strain) can learn to run this type of maze in a box without any special coloring in an average of 25 trials, with a variance of 64, and a normal distribution. The mean number of trials to learn the maze, for the rats tested with the colorful wallpaper, is 11.
What is the μ_M?

A)8
B)11
C)25
D)64

Question 8

The standard deviation of a distribution of means is sometimes called "the standard error of the mean," or the "standard error," because

A)it is an inaccurate estimate of a sample standard deviation and cannot be used to determine the variance.
B)it is calculated by summing the errors figured by subtracting sample means from the population variance.
C)it is frequently used as an "error term" when calculating the estimated sample variance.
D)it represents the degree to which particular sample means are "in error" as estimates of the mean of the population of individual scores.

Question 9

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 10

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

A)unimodal and symmetrical.
B)bimodal and symmetrical.
C)unimodal and skewed.
D)rectangular and symmetrical.

Question 11

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

A)it is based on fewer individuals than is the original population.
B)it is an estimate of the sample parameters rather than of the original population.
C)extreme scores are less likely to affect a distribution of means.
D)the mean of a distribution of means is so different than the population mean.

Question 12

Your sample of 12 people is being compared to a known population with a mean of 200 and a variance of 36.What is the variance of the distribution of means?

A)0.50
B)0.71
C)1.73
D)3.00

Question 13

As the number of people in a sample gets larger,the distribution of means

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

Question 14

In principal,a distribution of means can be formed by

A)calculating 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 μ.
D)randomly taking a very large number of samples from a population,each of the same size,and making a distribution of their means.

Question 15

The comparison distribution for the mean of a sample is the distribution of means because

A)comparing the mean of a sample to a distribution of a population of scores of individuals 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 research hypothesis.

Question 16

Dividing the variance of the population of individuals by the number of individuals in each sample yields

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 17

An experimental psychologist is interested in whether the color of an animal's surroundings affects learning rate. He tests 16 rats in a box with colorful wallpaper. The average rat (of this strain) can learn to run this type of maze in a box without any special coloring in an average of 25 trials, with a variance of 64, and a normal distribution. The mean number of trials to learn the maze, for the rats tested with the colorful wallpaper, is 11.
What is σ_M?

A)
B)
C)
D)

Question 18

The standard deviation of a distribution of means is

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

Question 19

In hypothesis testing,after figuring the Z score for the sample's mean,the next step would be to compare this Z score to

A)the parameters of the known population distribution.
B)an estimated distribution 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 be found if the null hypothesis were true.

Question 20

An experimental psychologist is interested in whether the color of an animal's surroundings affects learning rate. He tests 16 rats in a box with colorful wallpaper. The average rat (of this strain) can learn to run this type of maze in a box without any special coloring in an average of 25 trials, with a variance of 64, and a normal distribution. The mean number of trials to learn the maze, for the rats tested 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 will be 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 will be faster than the population of rats tested under ordinary circumstances.
C)The rate of learning for the population of rats tested with colorful wallpaper will be 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 will be faster than the population of rats tested under ordinary circumstances.

Question 21

A large school district is considering implementing a program that, if successful, would improve the reading scores of its students by 10 points. The current reading scores for the district are normally distributed with a mean of 37 and a standard deviation of 12. The administrators decide to test the new program in one school of 340 students.
What is the standard deviation of the comparison distribution?

A).42
B).65
C)12
D)144

Question 22

Anxiously-attached individuals in the general population tend to have low levels of satisfaction in their romantic relationships (μ = 10, σ = 5, positively skewed distribution). A therapist interested in increasing relationship satisfaction provides a week-long relaxation seminar to 11 anxious individuals. After completing the seminar, relationship satisfaction in the sample averages 12.
What is the comparison distribution's standard deviation?

A)0.45
B)0.67
C)1.51
D)2.27

Question 23

A large school district is considering implementing a program that, if successful, would improve the reading scores of its students by 10 points. The current reading scores for the district are normally distributed with a mean of 37 and a standard deviation of 12. The administrators decide to test the new program in one school of 340 students.
What is the predicted mean of the experimental distribution?

A)12
B)27
C)37
D)47

Question 24

A large school district is considering implementing a program that, if successful, would improve the reading scores of its students by 10 points. The current reading scores for the district are normally distributed with a mean of 37 and a standard deviation of 12. The administrators decide to test the new program in one school of 340 students.
What is the mean of the comparison distribution?

A)12
B)27
C)37
D)47

Question 25

A manufacturer who is considering the implementation of a one-week training program for all new employees decides to test the program with the next 100 employees hired, and then compare their productivity rate to the productivity rate of new employees based on past records—a rate that is normally distributed with a mean of 60 and a standard deviation of 8. The new program needs to produce a minimum improvement of 4 to be considered worthwhile.
What is the comparison distribution's standard deviation?

A)0.80
B)0.64
C)8
D)6.4

Question 26

Which of the following statistics would be the most likely to appear in a research article?

A)Z test
B)standard error
C)99% confidence interval
D)variance of the distribution of means

Question 27

The first thing that needs to be done to compute the 95% confidence interval is to

A)carry out the five steps of hypothesis testing.
B)find the 99% confidence interval and interpolate.
C)convert all scores to Z scores.
D)calculate the standard error.

Question 28

A manufacturer who is considering the implementation of a one-week training program for all new employees decides to test the program with the next 100 employees hired, and then compare their productivity rate to the productivity rate of new employees based on past records—a rate that is normally distributed with a mean of 60 and a standard deviation of 8. The new program needs to produce a minimum improvement of 4 to be considered worthwhile.
What is the mean of the comparison distribution?

A)52
B)60
C)68
D)100

Question 29

Anxiously-attached individuals in the general population tend to have low levels of satisfaction in their romantic relationships (μ = 10, σ = 5, positively skewed distribution). A therapist interested in increasing relationship satisfaction provides a week-long relaxation seminar to 11 anxious individuals. After completing the seminar, relationship satisfaction in the sample averages 12.
What is the shape of the comparison distribution?

A)positively skewed
B)negatively skewed
C)approximately normal
D)cannot be determined from the information provided

Question 30

A large school district is considering implementing a program that, if successful, would improve the reading scores of its students by 10 points. The current reading scores for the district are normally distributed with a mean of 37 and a standard deviation of 12. The administrators decide to test the new program in one school of 340 students.
What is the shape of the comparison distribution?

A)positively skewed
B)negatively skewed
C)approximately normal
D)cannot be determined from the information provided

Question 31

The 99% confidence interval is the region in a group of scores that

A)a psychologist can be 99% confident includes the true population mean.
B)a psychologist can be 1% confident includes the true population mean.
C)includes 49% of the scores below the mean and 50% of the scores above the mean.
D)includes 50% of the scores below the mean and 49% of the scores above the mean.

Question 32

Supporters of accepting results that reach only "marginal significance" argue that

A)the standard .05 significance level is an arbitrary convention.
B)hypothesis testing is an all or nothing decision.
C)the standard .05 and .01 significance levels are overly liberal.
D)hypothesis testing should use the most conservative criterion possible.

Question 33

The upper and lower ends of a confidence interval are the

A)interval estimates.
B)certainty brackets.
C)multi-point estimates.
D)confidence limits.

Question 34

Which of the following statements regarding confidence intervals is FALSE?

A)Confidence intervals are misused more often than significance tests.
B)Confidence intervals can be used in hypothesis testing.
C)Confidence intervals emphasize numerical estimates.
D)Confidence intervals are sometimes reported in research articles.

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

Which of the following would usually be considered "marginally significant"?

A)p < .001
B)p < .0
C)p < .05
D)p < .10

Question 37

A 95% confidence interval is figured by finding

A)the Z score for the bottom 5% of the distribution.
B)the Z score for the upper 95% of the distribution.
C)the cutoff points for the lower 2.5% and the upper 2.5% of the distribution.
D)the cutoff points for the lower 5% and the upper 5% of the distribution.

Question 38

A manufacturer who is considering the implementation of a one-week training program for all new employees decides to test the program with the next 100 employees hired, and then compare their productivity rate to the productivity rate of new employees based on past records—a rate that is normally distributed with a mean of 60 and a standard deviation of 8. The new program needs to produce a minimum improvement of 4 to be considered worthwhile.
What is the predicted mean of the experimental distribution?

A)52
B)60
C)64
D)100

Question 39

An experimental psychologist is interested in whether the color of an animal's surroundings affects learning rate. He tests 16 rats in a box with colorful wallpaper. The average rat (of this strain) can learn to run this type of maze in a box without any special coloring in an average of 25 trials, with a variance of 64, and a normal distribution. The mean number of trials to learn the maze, for the rats tested with the colorful wallpaper, is 11.
If the mean score of the sample is more extreme than the cutoff score on the comparison distribution,the psychologist will conclude that

A)the null hypothesis that the rats in the sample will learn more is supported.
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

Anxiously-attached individuals in the general population tend to have low levels of satisfaction in their romantic relationships (μ = 10, σ = 5, positively skewed distribution). A therapist interested in increasing relationship satisfaction provides a week-long relaxation seminar to 11 anxious individuals. After completing the seminar, relationship satisfaction in the sample averages 12.
What is the corresponding Z score for the sample's mean score on the comparison distribution?

A)0.66
B)1.32
C)0.44
D)1.74

Question 41

use the following information. A population is normally distributed with μ = 50,σ = 8,and N = 10.
If the sample mean is 45,the upper limit for the 95% confidence interval is __________.

Question 42

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

Question 43

use the following information. A population is normally distributed with μ = 50,σ = 8,and N = 10.
If the sample mean is 45,the lower limit for the 99% confidence interval is __________.

Question 44

use the following information. One hundred people are included in a study in which they are compared to a known population that has a mean of 73,a standard deviation of 20,and a rectangular distribution.
If the sample mean is 75,the lower limit for the 95% confidence interval is __________.

Question 45

use the following information. One hundred people are included in a study in which they are compared to a known population that has a mean of 73,a standard deviation of 20,and a rectangular distribution.
If the sample mean is 75,the lower limit for the 99% confidence interval is __________.

Question 46

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

Question 47

use the following information. One hundred people are included in a study in which they are compared to a known population that has a mean of 73,a standard deviation of 20,and a rectangular distribution.
__________.

Question 48

use the following information. A population is normally distributed with μ = 50,σ = 8,and N = 10.
The shape of the distribution of means in this example is __________.

Question 49

use the following information. A population is normally distributed with μ = 50,σ = 8,and N = 10.
The mean of the distribution of means = __________.

Question 50

use the following information. One hundred people are included in a study in which they are compared to a known population that has a mean of 73,a standard deviation of 20,and a rectangular distribution.
__________.

Question 51

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

Question 52

use the following information. One hundred people are included in a study in which they are compared to a known population that has a mean of 73,a standard deviation of 20,and a rectangular distribution.
The shape of the comparison distribution is __________.

Question 53

σ²_M represents the __________.

Question 54

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

Question 55

The comparison distribution when testing a hypothesis involving a sample of more than one participant is a(n)__________.

Question 56

use the following information. One hundred people are included in a study in which they are compared to a known population that has a mean of 73,a standard deviation of 20,and a rectangular distribution.
If the sample mean is 75,the upper limit for the 99% confidence interval is __________.

Question 57

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

Question 58

use the following information. One hundred people are included in a study in which they are compared to a known population that has a mean of 73,a standard deviation of 20,and a rectangular distribution.
If the sample mean is 75,the upper limit for the 95% confidence interval is __________.

Question 59

use the following information. A population is normally distributed with μ = 50,σ = 8,and N = 10.
The variance of the distribution of means = __________.

Question 60

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 61

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 see if the SAT scores for students at the school were different from the advertised average and found that the average SAT verbal score for 80 graduating seniors was 532.Using the .05 significance level,what should the PTA conclude about the school's claim?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Advanced topic: 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.Advanced topic: Explain the logic and computation of the confidence intervals.

Question 62

A 95% confidence interval will be __________ a 90% confidence interval.

Question 63

The lines that appear above the tops of the bars in a bar graph in a research article are __________.

Question 64

A school psychologist was interested in whether the 12 students in the chess club had a higher or lower mean grade point average (GPA)than the other students at a school.The overall GPA at the school was 2.55 with a standard deviation of 0.5; the distribution of GPAs was approximately normal.The average GPA of students in the chess club was 2.76.Using the .05 significance level,did the chess club represent a population that was different from students in general at this school?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Advanced topic: 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.Advanced topic: Explain the logic and computation of the confidence intervals.

Question 65

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

Question 66

The head of public safety notices that the average driving speed at a particular intersection averages 35 mph with a standard deviation of 7.5 mph.After a school speed limit sign of 20 mph is placed at the intersection,the first 40 cars travel past at an average speed of 32 mph.Using the .01 significance level,was there a significant change in driving speed?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Advanced topic: Figure the confidence limits for the 99% 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.Advanced topic: Explain the logic and computation of the confidence intervals.

Question 67

A result that is significant at p < .10 may be referred to as __________.

Question 68

A health psychologist knew that corporate executives in general have an average score of 80 with a standard deviation of 12 on a stress inventory and that the scores are normally distributed.In order to learn whether corporate executives who exercise regularly have lower stress scores,the psychologist measured the stress of 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.Sketch the distributions involved.
c.Advanced topic: 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.Advanced topic: Explain the logic and computation of the confidence intervals.

Question 69

A school psychologist interested in the effect of a program designed to reduce adjustment problems in newly transferred students knew from her years of working at the school that the average score on a scale of adjustment difficulties for transfer students was 58 with a standard deviation of 10.After starting the program,the psychologist tested 50 students and found their mean to be 52.Using the .01 level of significance,was this difference significant?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Advanced topic: Figure the confidence limits for the 99% 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 mean-what it is,the logic of how it is figured-and its role in the overall hypothesis testing process.Advanced topic: Explain the logic and computation of the confidence intervals.

Question 70

A psychology professor of a large class became curious as to whether the students who turned in 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 students to turn in tests was 78.Using the .05 significance level,was the average test score earned by the first 20 students to turn in their tests significantly different from the overall mean?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Advanced topic: 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.Advanced topic: Explain the logic and computation of the confidence intervals.

Question 71

The hypothesis testing procedure used when there is a single sample and a known population is a(n)__________.