Chapter 5 review questions with answer key PDF

Preview

Summary

Download Chapter 5 review questions with answer key PDF

Description

PSYC 2210: Review Questions Chapter 5: Hypothesis Test with Means of Samples Name: _________________________________________ Note: Some problems require the normal curve table, which can be copied from the textbook's Appendix (Table A–1). I.

MULTIPLE CHOICE

1) 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. 2) 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. 3) 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 4) 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. 5) 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.

6) 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. 7) 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. 8) 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 9) 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. 10) 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. 11) 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. 12) 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.

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. 14) 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. 15) 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. 16) When hypothesis testing with a sample of two or more, the formula for figuring your sample's score on the comparison distribution is A) Z = (M – μ) / σ B) Z = (M – μM) / σM C) Z = (X – μ) / σ D) Z = (X – μM) / σM Questions 17 – 21 are based on the following scenario. An experimental psychologist is interested in whether the colour of an animal's surroundings affects learning rate. She tests 16 rats in a box with colourful wallpaper. The average rat (of this strain) can learn to run this type of maze in a box without any special colouring 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 colourful wallpaper, is 11. 17) What is the null hypothesis? A) The rate of learning for the sample of rats tested with colourful 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 colourful 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 colourful 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 colourful wallpaper will be faster than the population of rats tested under ordinary circumstances. 18) What is the μM? A) 8 B) 11 C) 25 D) 64 19) What is σM?

A) B) C) D)

64/16 = 4.00 √(64/16) = 2.00 64/11 = 5.82 √(64/11) = 2.41

20) 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. 21) 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. Questions 22 – 25 are based on the following scenario. A 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. 22) What is the mean of the comparison distribution? A) 12 B) 27 C) 37 D) 47 23) What is the standard deviation of the comparison distribution? A) .42 B) .65 C) 12 D) 144 24) 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 25) What is the predicted mean of the experimental distribution? A) 12 B) 27 C) 37 D) 47 Questions 26 – 28 are based on the following scenario.

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. 26) What is the comparison distribution's standard deviation? A) 0.45 B) 0.67 C) 1.51 D) 2.27 27) 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 28) 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 Questions 29 – 31 are based on the following scenario. 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. 29) What is the mean of the comparison distribution? A) 52 B) 60 C) 68 D) 100 30) What is the comparison distribution's standard deviation? A) 0.80 B) 0.64 C) 8 D) 6.4 31) What is the predicted mean of the experimental distribution? A) 52 B) 60 C) 64 D) 100 32) Which of the following would usually be considered "marginally significant"?

A) B) C) D)

p < .001 p < .0 p < .05 p < .10

33) 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. 34) 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 35) The upper and lower ends of a confidence interval are the A) interval estimates. B) certainty brackets. C) multi-point estimates. D) confidence limits. 36) 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. 37) 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. 38) 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. 39) 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. 40) Which of the following statements regarding confidence intervals is FALSE?

A) B) C) D)

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

II. FILL IN THE BLANKS 41) The comparison distribution when testing a hypothesis involving a sample of more than one participant is a(n) _____________________________. 42) 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. 43) The mean of a distribution of means is ________________________the mean of the population. 44) There is no reason for the mean of a distribution of means to be larger or smaller than the _____________________. 45) σ2M represents the _________________________. 46) Another name for the standard deviation of a distribution of means is the __________________________. 47) The variance of a distribution of means equals the variance of the population of individuals divided by _______________________________. 48) The standard deviation of a distribution of means is the square root of the variance of _________________________. For questions 49 – 53, use the following information: A population is normally distributed with μ = 50, σ = 8, and N = 10. 49) The mean of the distribution of means = __________.

50) The variance of the distribution of means = __________.

51) The shape of the distribution of means in this example is _______________________. 52) If the sample mean is 45, the lower limit for the 99% confidence interval is _______________________.

53) If the sample mean is 45, the upper limit for the 95% confidence interval is _____________________.

For questions 54 – 60, 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 normal distribution. 54) μM = __________.

55) σM = __________.

56) The shape of the comparison distribution is _______________. 57) If the sample mean is 75, the lower limit for the 99% confidence interval is __________.

58) If the sample mean is 75, the upper limit for the 99% confidence interval is __________.

59) If the sample mean is 75, the lower limit for the 95% confidence interval is __________.

60) If the sample mean is 75, the upper limit for the 95% confidence interval is __________.

61) A distribution of means will be approximately normal so long as there are at least __________ scores in the sample. 62) A result that is significant at p < .10 may be referred to as ___________________________________________________.

63) The lines that appear above the tops of the bars in a bar graph in a research article are ________________________________________. 64) The hypothesis testing procedure used when there is a single sample and a known population is a(n) _____________. 65) A 95% confidence interval will be _______________________ a 90% confidence interval.

III.

PROBLEM SOLVING: HYPOTHESIS TESTING (Z-TEST)

66) 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. a. Figure the confidence limits for the 95% confidence interval. (it might be helpful to know the logic and computation of the confidence intervals)

67) 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. Figure the confidence limits for the 95% confidence interval. 68) 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. Figure the confidence limits for the 99% confidence interval. 69) 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. Figure the confidence limits for the 95% confidence interval.

70) 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. Figure the confidence limits for the 95% confidence interval. 71) 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. Figure the confidence limits for the 99% confidence interval.

Chapter 5 Hypothesis Test with Means of Samples Answer Key I. Multiple choice 1 A 2 D 3 C 4 C 5 A 6 C 7 B 8 9 10

D D B

II. Fill in the blanks 41 Distribution of means

11 12 13 14 15 16 17

A C B D A B C

21 22 23 24 25 26 27

C C B C D C B

31 32 33 34 35 36 37

C D A B D C A

18 19 20

C B C

28 29 30

D B A

38 39 40

A D A

30

51

normal

61

99% CI has a critical value (z-score) of 2.58; SE (M = 8/10) is 2.5298; Margin of error (ME = 2.58 x 2.5298) is 6.5269 so; Lower limit : (M – ME) or M – 2.58 (/N) 45 – 6.5269 = 38.47 95 % CI has a critical value (z-score) of 1.96; Upper limit : M + 1.96 (/N) 45 + 1.96 (8/10) 45 + 1.96 (2.5...