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Chapter 5 Introduction to Hypothesis Testing

1) Which of the following statements is most accurate about hypothesis testing?

- A) It is a central theme in the statistical analysis of virtually all social science research.
- B) It is a simple part of statistics that applies to approximately three statistical procedures.
- C) It is a fairly uncommon way of using statistics.
- D) It is a kind of statistical procedure that is used mainly as part of descriptive statistics.

Answer: A

2) What is a hypothesis?

- A) a procedure for using descriptive statistics in research
- B) a set of theories about certain facts, relationships, or events
- C) a prediction about the results of a research study
- D) a way of quantifying the normal curve

Answer: C

3) A _________________ is a set of principles that attempts to explain one or more facts, relations, or events.

- A) curve
- B) table
- C) theory
- D) deviation

Answer: C

4) A theory usually gives rise to various specific _____________ that can be tested in research studies.

- A) t tests
- B) hypotheses
- C) Z scores
- D) formulations

Answer: B

5) You want to know if a new employee incentive program really works. How would you test the hypothesis that it does work?

- A) Try to disprove the hypothesis that it does work
- B) Try to prove the hypothesis that it does work
- C) Try to disprove the hypothesis that it does not work
- D) Try to prove the hypothesis that it does not work

Answer: C

6) How do you set up a hypothesis testing problem?

- A) You set it up to test what you predict will happen
- B) You set it up to test the opposite of what you predict will happen
- C) You set up two problems, one to test what you predict and the other to test the opposite
- D) You set up a test that assumes the two populations are different, regardless of whether that is what you predict or not

Answer: B

7) A researcher tests whether a new teaching method is more effective than the old one. What is the RESEARCH hypothesis?

- A) The new teaching method is more effective than the old teaching method.
- B) The old teaching method is more effective than the new teaching method.
- C) There is no difference in effectiveness between the old teaching method and the new teaching method.
- D) There is some difference in effectiveness between the old teaching method and the new teaching method, but which is more effective is not predicted.

Answer: A

8) A researcher tests whether there is any difference between how fast people work in the morning versus how fast they work in the evening. What is the NULL hypothesis?

- A) People who work in the morning work faster.
- B) People who work at night work faster.
- C) There is some difference, but which is faster is not predicted.
- D) There is no difference in the speed at which people work.

Answer: D

9) A researcher tests effects of a new training program. The hypothesis that this new training program will work better than the old training program is called the:

- A) comparison hypothesis
- B) research hypothesis
- C) null hypothesis
- D) there is no special name for this kind of a hypothesis

Answer: B

10) A researcher wants to know if a new type of health insurance works better or worse than a standard form of health insurance. The hypothesis that there will be no difference between the new type of insurance and the old type of insurance is called the:

- A) comparison hypothesis
- B) research hypothesis
- C) null hypothesis
- D) functional differential

Answer: C

11) You determine the characteristics of the comparison distribution to answer which of the following questions?

- A) Given a particular sample value, what is the probability of obtaining that value if the research hypothesis is true?
- B) Given a particular sample value, what is the probability of obtaining that value if the null hypothesis is true?
- C) Given a particular population value, what is the probability of obtaining that value if the research hypothesis is true?
- D) Given a particular population value, what is the probability of obtaining that value if the null hypothesis is false?

Answer: B

12) What represents the situation in which the null hypothesis is true?

- A) the comparison distribution
- B) the directional distribution
- C) the nondirectional distribution
- D) a one-tailed test

Answer: A

13) A sample is studied to see if it represents a population (called Population 1) that is different from a known population (called Population 2). The comparison distribution is:

- A) the same as the distribution of Population 1
- B) the same as the distribution of Population 2
- C) a rectangular distribution with the same mean and standard deviation as

Population 1 - D) a rectangular distribution with the same mean and standard deviation as

Population 2

Answer: B

14) Place the five steps of the hypothesis-testing process in the correct order:

1. Determine the characteristics of the comparison distribution.

2. Decide whether to reject the null hypothesis.

3. Restate the question as a research hypothesis and a null hypothesis about the populations.

4. Determine your sample’s score on the comparison distribution.

5. Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected.

- A) 2, 4, 1, 5, 3
- B) 3, 4, 1, 5, 2
- C) 1, 3, 5, 4, 2
- D) 3, 1, 5, 4, 2

Answer: D

For the following question(s): A researcher is interested in a new kind of exercise. This new exercise can be done by anyone because it does not require any equipment, and therefore could be potentially beneficial without cost to the person. The researcher is interested in whether this new exercise will reduce the rate of heart attacks in the people who participate in doing it.

15) What is the research hypothesis?

- A) People will participate because it does not cost them any money.
- B) The exercise will make no difference in the rate of heart attacks.
- C) The exercise will reduce the rate of heart attacks.
- D) The exercise will increase the rate of heart attacks.

Answer: C

16) What is the null hypothesis?

- A) People will participate because it does not cost them any money.
- B) The exercise will make no difference in the rate of heart attacks.
- C) The exercise will reduce the rate of heart attacks.
- D) The exercise will increase the rate of heart attacks.

Answer: B

17) What is the comparison distribution?

- A) The distribution of those who participate in the exercise program.
- B) The distribution of those who do not participate in the exercise program.
- C) The distribution of those who have heart attacks.
- D) The distribution of those who do not have heart attacks.

Answer: B

18) What is the “cutoff on the comparison distribution”?

- A) The point at which, assuming the null hypothesis is true, it would be extremely unlikely to get a result this extreme.
- B) The point at which, assuming the research hypothesis is true, it would be extremely unlikely to get a result this extreme.
- C) The point at which the comparison distribution ends.
- D) The point at which you accept the null hypothesis if the result is more extreme.

Answer: A

19) Another name for the research hypothesis is the:

- A) null hypothesis
- B) statistical hypothesis
- C) void hypothesis
- D) alternative hypothesis

Answer: D

20) The logic of hypothesis testing involves figuring out the probability of getting a particular result if:

- A) the research hypothesis is true
- B) the sampling distribution is accurate
- C) the comparison distribution is true
- D) the null hypothesis is true

Answer: D

21) The cutoff sample score is also known as the:

- A) critical value
- B) sampling distribution
- C) null value
- D) sample Z score

Answer: A

22) What does it mean if a researcher said she rejected the null hypothesis at the .05 level?

- A) There was less than a 5% chance that she would have gotten such an extreme result by chance if the null hypothesis were true.
- B) There was more than a 5% chance that she would have gotten such an extreme result by chance if the null hypothesis were true.
- C) There is a 5% chance that there is a difference between the two populations she is testing if the null hypothesis were true.
- D) There is a 95% chance that the research hypothesis is true.

Answer: A

23) What are the generally accepted cutoff points (or conventional levels of significance) in hypothesis testing in psychology?

- A) .001 and .10
- B) .01 and .05
- C) .10, .20, and .30
- D) .05, .25, and .95

Answer: B

24) Based on the results of his study, a researcher rejects the null hypothesis because the probability of obtaining his result if the null hypothesis were true is less than 5%. How would this be symbolized?

- A) p = 5%
- B) p < .05
- C) .05 < p
- D) p > 5%

Answer: B

25) A result is considered statistically significant when a sample value is so extreme that:

- A) the research hypothesis is rejected
- B) the null hypothesis is accepted
- C) the research hypothesis is accepted
- D) the null hypothesis is rejected

Answer: D

26) How do you determine whether or not to reject the null hypothesis?

- A) If the Z score is less than -1 or greater than +1
- B) If the Z score is greater than +2.5
- C) Compare the Z score needed to reject the null hypothesis to the actual sample Z score
- D) Compare the standard deviation of the sample to the standard deviation of the population

Answer: C

27) Suppose the cutoff Z score on the comparison distribution is ±2.31. You could reject the null hypothesis if the sample value’s Z score on this distribution was:

- A) -16
- B) -41
- C) 16
- D) 83

Answer: D

28) The cutoff Z score on the comparison distribution is 1.64 and the sample value has a score of 1.32 on the comparison distribution.

- A) the null hypothesis cannot be rejected
- B) the null hypothesis is rejected
- C) the research hypothesis is supported
- D) the research hypothesis is rejected

Answer: A

29) If the null hypothesis is rejected, the researcher can conclude that the results:

- A) support the research hypothesis
- B) prove that the research hypothesis is true
- C) were inconclusive
- D) support the null hypothesis

Answer: A

30) Why can a researcher not say that the results PROVE that the research hypothesis is true?

- A) Because the results of research studies are based on probabilities
- B) Because the results of research studies are generally incorrect
- C) Because it is likely that the results will be disproved within a short time
- D) All of the above

Answer: A

31) The results of a study are not extreme enough to reject the null hypothesis. What can the researcher conclude with reasonable confidence?

- A) Results support the null hypothesis.
- B) Results prove that the null hypothesis is true.
- C) Results support the research hypothesis.
- D) None of the above; the results are inconclusive.

Answer: D

32) Which of the following is NOT a correct statement of one of the five steps of hypothesis testing?

- A) Restate the question as a research hypothesis and a null hypothesis about the populations.
- B) Determine the characteristics of the comparison distribution.
- C) Determine the cutoff score on the sample distribution at which the research hypothesis should be rejected.
- D) Decide whether to reject the null hypothesis.

Answer: C

33) A researcher wants to know if a new type of exercise improves peoples’ health. Would this be a one-tailed or two-tailed test and why?

- A) One-tailed because the study is only interested in whether the exercise increases health
- B) One-tailed because the study only looks at the effects of exercise and does not take other factors into account
- C) Two-tailed because they will have to study healthy and unhealthy people
- D) Two-tailed because there is no predicted direction of difference

Answer: A

34) Suppose that a researcher wants to know if a new flu drug affects people, either by making them better or worse. Would this be a one-tailed or two-tailed test and why?

- A) One-tailed because only one issue is discussed—the drug
- B) One-tailed because there is only one interaction, which is between the flu and the drug
- C) Two-tailed because there are two variables—whether or not people take the drug and how their flu is affected
- D) Two-tailed because there is no predicted direction of the effect of the drug

Answer: D

35) A one-tailed test is especially associated with:

- A) the research hypothesis
- B) the null hypothesis
- C) a nondirectional hypothesis
- D) a directional hypothesis

Answer: D

36) What is a correct argument for using a two-tailed test even if there is a clear basis for predicting a result in a given direction?

- A) If the null hypothesis is in fact true, a failure to reject it will give stronger evidence in support of it.
- B) One-tailed tests cannot be used in almost any real study involving two groups.
- C) If an unexpected result comes out opposite to what is predicted, it does not have to be ignored.
- D) A two-tailed test gives you a better chance of getting a significant result.

Answer: C

37) What is the argument for using a one-tailed test when there is a clear basis for predicting a result in a given direction?

- A) The underlying mathematics of one-tailed tests are more accurate.
- B) If the result is opposite to the prediction, the researcher can still do a two-tailed test later.
- C) It is more conservative, in the sense that in using a one-tailed test it is harder to reject the null hypothesis.
- D) A particular theory is being tested, and if the results come out opposite to the theory, that adds no more information than if the result simply had not been significant.

Answer: D

38) A researcher reported significant results for a study, noting that “.05 > p.” What is NOT standard about this expression?

- A) “.05” should have been written as “5%”
- B) “p” should be Z
- C) “.05 > p” should have been written “p < .05”
- D) nothing is wrong with this expression (it is standard)

Answer: C

39) Which of the following is a standard way for the significance level of the result of a hypothesis test to be reported in a research article?

- A) p < .01
- B) p = .03
- C) p < .05
- D) all of the above are standard and can be used

Answer: D

40) There is a special complication when using a two-tailed test. The researcher must:

- A) multiply the significance percentage by .05
- B) divide the significance percentage by .05
- C) divide up the significance percentage between the two tails of the distribution
- D) divide up the significance percentage by the four quartiles of the distribution

Answer: C

41) For a two-tailed test at the .05 significance level, the appropriate cutoff Z scores would be:

- A) -96 and +1.96
- B) -58 and +2.58
- C) -64 and +1.64
- D) -33 and +2.33

Answer: A

42) In most behavioral and social science research articles, unless the researcher specifically states that a __________ test was used, it is assumed that it was a __________.

- A) two-tailed; one-tailed
- B) .10 significance test; .25 significance test
- C) .05 significance test; .01 significance test
- D) one-tailed; two-tailed

Answer: D

43) Setting the significance level cutoff at .10 instead of the more usual .05 increases the likelihood of:

- A) a Type I error
- B) a Type II error
- C) failing to reject the null hypothesis
- D) accepting the null hypothesis when, in fact, it is false

Answer: A

44) A Type I error is the result of:

- A) improper measurement techniques on the part of the researcher
- B) failing to reject the null hypothesis when, in fact, it is true
- C) incorrectly rejecting the null hypothesis
- D) incorrectly accepting the null hypothesis

Answer: C

45) Setting the significance level at a very extreme cutoff (such as .001) increases the chances of:

- A) getting a significant result
- B) rejecting the null hypothesis
- C) a Type I error
- D) a Type II error

Answer: D

46) Failing to reject the null hypothesis when the research hypothesis is true is referred to as:

- A) the probability of rejection
- B) the error term
- C) a Type I error
- D) a Type II error

Answer: D

47) Type II errors concern scientists because:

- A) it could mean that a good theory or beneficial practice is not used
- B) it means that the experiment must be repeated to confirm the positive result
- C) rejecting the null hypothesis should only occur when the research hypothesis is true
- D) future researchers might build entire theories based on a mistakenly significant result

Answer: A

48) Conventional levels of significance have been set at 5% and 1% in order to:

- A) maximally protect against Type I error
- B) maximally protect against Type II error
- C) compromise between the risk of a Type I and Type II error
- D) none of the above; these levels were set historically in an arbitrary way without regard to issues associated with Type I or Type II error

Answer: C

49) Decision errors are possible in hypothesis testing because you are making decisions about _______ based on information in ________.

- A) distributions; Z tables
- B) populations; samples
- C) samples; populations
- D) distributions; frequency tables

Answer: B

50) Suppose you conduct a study in which you set the significance level cutoff at a lenient probability level, such as 15%. In this case, you would have a 15% chance of making a:

- A) Type I error
- B) Type II error
- C) Type III error
- D) computational error

Answer: A

51) Complete the table with the correct and incorrect decision-making terms in hypothesis testing:

- A) 1 = Type I error; 2 = correct decision; 3 = Type II error; 4 = computational error
- B) 1 = correct decision; 2 = Type I error; 3 = Type II error; 4 = correct decision
- C) 1 = Type I error; 2 = correct decision; 3 = correct decision; 4 = Type II error
- D) 1 = computational error; 2 = Type I error; 3 = Type II error; 4 = correct decision

Answer: C

52) Match the term on the left with its correct definition on the right:

- A) decision error 1) rejecting the null hypothesis when in fact it is true
- B) Type I error 2) the levels of significance widely used in the behavioral and social sciences
- C) Type II error 3) incorrect conclusion in hypothesis testing in relation to the real (but unknown) situation, such as deciding the null hypothesis is false when it is really true
- D) conventional levels of 4) failing to get a statistically significant result

significance when in fact the research hypothesis is true

Answer: A-3; B-1; C-4; D-2

53) A researcher is interested in the effect of going through a terrorist attack on the attitude of police officers about the goodness of people in New York City. After the attack, police may hold more positive attitudes about people (because of various acts of heroism and altruism exhibited by residents) or more negative attitudes because of negative outcomes (looting and dishonesty after the event). What type of hypothesis should the researcher make?

- A) directional
- B) significant
- C) percentile
- D) nondirectional

Answer: D

54) The usual rule in statistics is that a study cannot find the null hypothesis to be true—one can only reject or fails to reject the null hypothesis is simply uninformative and such studies tend not to be published. Why is this a problem in the field of psychology and other behavioral sciences?

- A) Much work could be avoided if people knew what interventions had not worked.
- B) This may lead to ideas being assumed as true just because a few studies found results supporting them (while many more, unreported, had not).
- C) Power and effect size considerations are getting ignored.
- D) Both A and B are correct.

Answer: D

55) When a result is close but does not reach the significance level chosen , if may be reported as a “near significant trend” or as having “approached significance,” with, for example,

p < .10. (True or False)

Answer: TRUE

56) __________ is a procedure for deciding whether the outcome of a study (results for a sample) supports a particular theory or practical innovation (which is thought to apply to a population).

Answer: Hypothesis testing

57) In hypothesis testing, a statement about the predicted relation between populations (often a prediction of difference between population means) is called the __________.

Answer: research hypothesis

58) In hypothesis testing, a statement that there is no difference between populations (or a difference opposite to that predicted) is called the __________.

Answer: null hypothesis

59) In hypothesis testing, if the null hypothesis is rejected, this is taken as support for the __________.

Answer: research hypothesis

60) A __________ is a prediction about the results of a research study.

Answer: hypothesis

61) In hypothesis testing, the __________ is the distribution to which you compare the score attained in your actual sample (based on the study results).

Answer: comparison distribution

62) The __________ distribution represents the situation if the null hypothesis is true.

Answer: comparison; population 2

63) Before conducting a study, a researcher determines the cutoff sample score on the __________ distribution at which the null hypothesis would be rejected if the sample is more extreme than this cutoff score.

Answer: comparison; population 2

For the following question(s): A study tests the prediction that people who spend a great deal of time on the beach have more eye problems than people in general.

64) Population 1 refers to __________. Population 2 refers to people in general.

Answer: people who spend a great deal of time on the beach

65) The research hypothesis is __________.

Answer: People who spend a great deal of time on the beach have more eye problems than people in general.

66) The null hypothesis is _________.

Answer: People who spend a great deal of time on the beach do not have more eye problems than people in general.

For the following question(s): A researcher wants to know whether people who listen regularly to radio talk shows are more or less likely to vote in national elections than are people in general.

67) The ________ is that there is no difference in voting between those who do and do not listen regularly to radio talk shows.

Answer: null hypothesis

68) The comparison distribution is based on the distribution of the voting behavior of _________.

Answer: people in general, Population 2

69) The researchers would use a(n) _________ -tailed test.

Answer: two

70) If the value of the sample is more extreme than the _________ on the comparison distribution, then the null hypothesis will be rejected.

Answer: cutoff, critical value

71) When the null hypothesis is rejected, the results of a study are said to be ________.

Answer: statistically significant, significant

72) If the cutoff represents the most extreme 5% of the comparison distribution, then 5% is called the __________ level.

Answer: significance, alpha

73) The 1% and 5% levels are the ________ levels of significance in behavioral and social science research.

Answer: conventional, most commonly used

74) Most behavioral and social scientists use the ________ significance level, but those wanting to be more conservative commonly use the ________ levels.

Answer: .05; .01 or .001 (5%; 1% or .1%)

75) A(n) __________ hypothesis is a research hypothesis predicting that one population will have higher scores than the other.

Answer: directional

76) When testing a directional hypothesis, you use a(n) ________ test.

Answer: one-tailed

77) In a(n) _________, the region of the comparison distribution in which the null hypothesis would be rejected is all on one side of the distribution.

Answer: one-tailed test, test of a directional hypothesis

78) A research hypothesis that does not predict a particular direction of difference between populations is called a(n) ________ hypothesis.

Answer: nondirectional

79) A study is done with a sample of one person. The general population (Population 2) has a mean of 30 and a standard deviation of 5. The cutoff Z score for significance in this study is a Z of 1.96. The raw score of the sample person is 45. What should you conclude? __________.

Answer: Reject the null hypothesis, the research hypothesis is supported

80) A study is done with a sample of one person. In the general population (Population 2), Population M = 100 and Population SD = 8. The cutoff Z score for significance in this study is a Z of 1.64. The raw score of the sample is 110. What should you conclude? __________.

Answer: Do not reject the null hypothesis, the result is inconclusive

81) ________ is a way of saying in symbols that a research result is significant at the .05 level.

Answer: p < .05

82) Cutoff scores are more extreme with a one-tailed test. (True or False)

Answer: FALSE

83) The cutoff Z scores associated with a one-tailed test at the .05 significance level are _________.

Answer: -1.64 or +1.64

84) The cutoff Z scores associated with a two-tailed test at the .01 significance level are _________.

Answer: -2.58 and +2.58

85) Rejecting the null hypothesis when in fact it is true is a(n) __________.

Answer: Type I error

86) A Type I error occurs when you obtain a statistically significant result when in fact __________.

Answer: the research hypothesis is false, the null hypothesis is true

87) p < .05 means that there is less than a 5% chance of making a(n) _____.

Answer: Type I error

88) Researchers can always tell when they have made a Type I or Type II error. (True or False)

Answer: FALSE

89) Using the .01 level of significance instead of the .05 level decreases the chance of making a(n) _________.

Answer: Type I error

90) When it comes to setting significance levels, protecting against one kind of decision error decreases the chance of making the other. (True or False)

Answer: FALSE

91) Researchers who do not want to take a lot of risk set the significance level lower than .05, such as p < .001. (True or False)

Answer: TRUE

92) A(n) _________ occurs when you fail to reject the null hypothesis when in fact it is false.

Answer: Type II error

93) Researchers try to avoid making a(n) __________ because it could mean failing to make use of a practical procedure or useful theory.

Answer: Type II error

94) The significance level is the same as the chance of making a(n) ________.

Answer: Type I error

95) The outcomes of hypothesis testing sometimes are shown simply as _________ in a table or results.

Answer: asterisks

96) Do people give more money to street performers in certain U.S. city locations? To examine this issue, a street performer was randomly selected and asked to perform in one of these special U.S. city locations. The researcher found that the person earned significantly more than average and reported this result as “p < .05.” Explain these results to someone who is not familiar with hypothesis testing.

97) A researcher was interested in reducing the stress level of people on vacation who have been identified as having a “Type A personality.” She figured that by taking away the watch of one of these vacationers, his stress level should be reduced. She then recorded the average stress level of all the vacationing Type A people (in order to calculate an average) and compared her test participant to that average. His Z score was -1.93, which was significant at the .05 level. Explain this result to someone who is not familiar with hypothesis testing.

98) A sociologist was interested in whether a particular film reduced the amount of sex-role stereotyping done by college students. He first obtained a measure of the average amount of stereotyping reported on a particular test among normal college students. He then took a participant who had seen the film and compared that participant’s result on the test to the average. The obtained Z score (.23) was not significant at the .05 level. Explain this finding to a person who is not familiar with hypothesis testing.

99) A researcher who had been studying nonverbal communication became interested in whether she and her lab assistants had begun to use more than the average amount of nonverbal gestures. During a lab presentation, she measured the amount of this type of communication in one of her assistants. She then compared this assistant’s score to the average number of nonverbal gestures for people in the general population. She found that her assistant was, in fact, using a significantly higher amount of nonverbal communication (Z score of 4.25, which was significant at the .01 level). Explain this result.

100) A medical researcher is interested in determining whether a new medication for lung cancer is effective in a group of patients with early-stage disease. Explain what a Type I and Type II error would be in this study. (Be sure to state your answer in terms of the variables of this particular study.) What level of significance would you choose to utilize and why?

101) A researcher is interested in comparing the SAT scores of a group of gifted children (who are expected to score higher) with the population mean. Explain what a Type I and Type II error would be in this study. (Be sure to state your answer in terms of the variables of this particular study.)

102) A study is conducted of whether students with fewer extracurricular activities have a higher GPA than students in general. Explain what a Type I and Type II error would be in this study. (Be sure to state your answer in terms of the variables of this particular study.) What level of significance would you choose to utilize and why?

103) A study examines whether students who have been in a theology class score higher on a scale of religious beliefs than the average person. Explain what a Type I and Type II error would be in this study. (Be sure to state your answer in terms of the variables of this particular study.)

104) An education researcher conducts a study of whether children with a large vocabulary scored higher on an intelligence test than the average. Explain what a Type I and Type II error would be in this study. (Be sure to state your answer in terms of the variables of this particular study.)

105) What is a decision error? If you set a lenient significance level (e.g., .20), what is the effect on the probability of a Type I and Type II error? If you set a stringent significance level (e.g., .0001), what is the effect on the probability of at Type I and Type II error?

Answer: A decision error is a conclusion drawn from hypothesis testing that does not match reality; an incorrect conclusion in hypothesis testing in relation to the real (but unknown) situation, such as deciding the null hypothesis is false when it is really true. Decision errors are situations in which the right procedures lead to the wrong decisions.

- If you set a lenient significance level, the probability of a Type I error is high and the probability of a Type II error is low. If you set a stringent significance level, the probability of a Type I error is low and the probability of a Type II error is high.

For the following questions, please use all five steps of hypothesis testing:

- Restate the question as a research hypothesis and a null hypothesis about the populations.
- Determine the characteristics of the comparison distribution.
- Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected.
- Determine your sample’s score on the comparison distribution.
- Decide whether to reject the null hypothesis.

106) Do children from lower socioeconomic status (SES) neighborhoods have lower than average test-taking skills? A researcher administered a standard measure of test-taking skills to a randomly chosen child from a low-SES neighborhood and found him to have a score of 38. The average on this measure for the population in general is 50 with a standard deviation of 10. What should you conclude about whether those in low-SES neighborhoods have lower test-taking ability? (Use the .01 significance level.)

- Use the five steps of hypothesis testing.
- Sketch the distributions involved.
- Explain the logic of what you did (be sure your explanation includes the overall logic of hypothesis testing, including each of the five steps).

Answer: Cutoff (.05 level, one-tailed-low) = -2.33

Sample’s Z score on the comparison distribution = -1.20

Do not reject the null hypothesis; study is inconclusive

107) Does computer-assisted instruction help children with reading difficulties to learn reading skills at a faster than normal rate? A researcher arranged for one of these children to have access to a set of computer-learning programs instead of the normal reading curriculum for one term. At the end of the term, the researcher tested her on a standardized reading ability test on which the mean for children with reading difficulties is 36 with a standard deviation of 6. The test participant scored 47. Was this result significant at the .05 level?

- Use the five steps of hypothesis testing.
- Explain the logic of what you did (be sure your explanation includes the overall logic of hypothesis testing, including each of the five steps).

Answer: Cutoff (.05 level, one-tailed-high) = 1.64

Sample’s Z score on the comparison distribution = 1.83

Reject the null hypothesis; the research hypothesis is supported

108) A popular music magazine has speculated that the average length of a song on one of today’s popular CDs is 3.75 minutes with a standard deviation of .75 minutes. A randomly selected song of a particular new type of music is 5 minutes. Based on this one case, what can you conclude about whether this new type of music is longer than popular songs in general? (Use the .05 level.)

- Use the five steps of hypothesis testing.
- Sketch the distributions involved.
- Explain the logic of what you did (be sure your explanation includes the overall logic of hypothesis testing, including each of the five steps).
- Would the conclusion be different if you utilized the .01 level of significance?

Answer: Cutoff (.05 level, one-tailed-high) = 1.64.

Sample’s Z score on the comparison distribution = 1.67.

Reject the null hypothesis; the research hypothesis is supported.

If researcher had used the .01 level of significance (cutoff score of 2.33), the results would have been inconclusive.

109) An experimenter was interested in the accuracy of a new type of polygraph (lie detector) test. To test this, a polygraph operator used the machine on a participant who was told ahead of time to lie about some of the questions being asked. In an average situation of this type, the polygraph test is 75% accurate with a standard deviation of 6.5%. With the new machine the operator correctly identified 83.5% of the false responses. Is the accuracy of the new polygraph different from the usual ones? (Use the .05 level.)

- Use the five steps of hypothesis testing.
- Sketch the distributions involved.

Answer: Cutoff (.05 level, two-tailed) = +1.96

Sample’s Z score on the comparison distribution = 1.31

Do not reject the null hypothesis; study is inconclusive.

110) Do children raised in a communal environment differ from children in general in their ability to recognize emotional expression? A standard test of emotional expression shows a series of pictures of various facial expressions. In this series, the average child in the population in general can identify 14 with a standard deviation of 3. The researcher administers the picture test to a randomly selected child raised in a communal environment. The child was able to identify 16 expressions correctly. Based on this result, what should you conclude about whether being raised in a communal environment makes any difference in children’s ability to recognize emotional expression? (Use the .01 level.)

- Use the five steps of hypothesis testing.
- Sketch the distributions involved.

Answer: Cutoff (.01 level, two-tailed) = +2.58.

Sample’s Z score on the comparison distribution = .67.

Do not reject the null hypothesis; study is inconclusive.