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Statistics For The Behavioral And Social Sciences A Brief Course 6th Edition Arthur Aron Elliot J Blows Elaine N Aron - Solutions
A box contains A balls numbered 1,2,...,A, and n balls are drawn from it with replacement. What is the probability that k different balls are drawn?
A die is tossed repeatedly until all faces have appeared at least once.What is the probability that (a) the minimum number of tosses required is 12; (b) exactly 12 tosses are required?
A box contains k balls numbered 1,2,...,&. They are drawn one by one without replacement in succession. If X t is the number of the ball drawn at the /th stage, we say that a match occurs if X t = i, i = 1,2,...,&.Find the probability of (a) exactly r matches; (b) at least r matches.
Six men and six women are seated on a bench. What is the probability that men and women alternate? Does the result change if they are seated around a round table instead of a bench?
An urn contains A balls numbered 1,2,...,A; k balls are drawn from it with replacement. Find the probability that every number 1,2,...,A occurs at least once.
An urn A contains five balls numbered 1, four balls numbered 2, and seven balls numbered 3.Urn B x contains eight black and 10 white balls;urn B2 contains seven black and eight white balls; and urn B3 contains nine black and six white balls. One ball is drawn from A , and if the number on the ball
Two persons toss a coin 20 times each. What is the probability that they both obtain the same number of heads?
If four dice are tossed, what is the probability that:(a) The total of the face numbers is 15, 16, or 17?(b) The difference between the highest and the lowest face numbers is at least 3?
In a bridge game what is the probability that:(a) Each player has exactly one ace?(b) A player and his partner have three aces between them?(c) A player and his partner have k {k < 13) cards of a specified suit?(d) A hand has n x clubs, n2 diamonds, n3 hearts, and n4 spades, where+ n2 + n3 + n4 =
Urn Ux contains five white and three black balls; urn U2 contains four white and five black balls; and urn U3 contains three white and seven black balls.(a) One ball is drawn from each urn. What is the probability that two of them are black and one white?(b) An urn is selected at random and four
How many persons should there be in a group so that the probability of a repeated birthday in the group is greater than 1/2?
What is the probability that a group of 50 persons will have a repeated birthday?
Nine balls are distributed among four boxes. What is the probability that one of the boxes contain three balls?
Two urns Ux and U2 contain, respectively, five white and three black balls, and four white and four black balls. One ball is transferred from Ux to t/2, and thereafter one ball is drawn from U2. What is the probability that it is white?
Twenty tickets are numbered 1 to 20.What is the probability that four tickets taken in succession will bear numbers in an increasing or decreasing order?
What is the probability that in a bridge game a player and his partner have (a) all 13 cards of a specified suit; (b) all 13 cards of any suit?
Eight cards are drawn at random from a full deck of 52 cards. What is the probability that they contain (a) no ace; (b) at least one ace; (c)exactly two aces?
In poker, five cards are selected at random from a full deck of 52.What is the probability that a hand in a poker game contains a “pair,”two cards of the same face value?
What is the probability of obtaining (a) a total of 13 points when three dice are thrown; (b) two heads and three tails when five coins are tossed?
Three balls are drawn at random from an urn containing five white and four black balls. What is the probability that two of them are white and one is black?
Two urns, Ui and U2, contain, respectively, two white and three black balls, and three white and two black balls. One ball is transferred from Ux to U2 and thereafter (a) a ball is drawn from f/2, the event being that the ball is white; (b) two balls are drawn from t/2, the event being that one of
Each of three boxes, identical in appearance, has two drawers. The first box contains a gold coin in each drawer; the second contains a silver coin in each drawer; and the third contains a gold coin in one drawer and a silver coin in the other. Consider the following experiments: (1) a box is
A coin is tossed repeatedly until it shows a head. The event is that the head shows in less than 10 tosses.
Three different objects, 1, 2, and 3, are distributed at random on three different sites, marked 1,2, 3.The event is: (a) none of objects occupies the place corresponding to its number; (b) at least two of the objects occupy places corresponding to their numbers.
Six balls are distributed at random among three boxes, and the event is: (a) the first box contains three balls; (b) one of the boxes contains two balls; (c) none of the boxes is empty.
Two cards are drawn without replacement from a deck of well-shuffled cards. The event is: (a) both the cards are aces; (b) one of the cards is an ace.
In Exercise 5, the students are chosen with replacement and the event is as in Exercise 5.
A class contains 10 students, four of them being Canadians, three Englishmen, two Americans, and one Italian. Three students are chosen without replacement. The event is obtaining at least two Canadians.
An urn contains three white and two black balls. Consider the following experiments: (1) two balls are drawn simultaneously from the urn; (2)two balls are drawn one after the other from the urn without replacement; and (3) two balls are drawn one after the other from the urn with replacement. For
An urn contains five white, seven black, and 10 green balls. One ball is drawn from the urn. The event is: (a) the ball is white; (b) the ball is not green.
Three dice are thrown, and the event is: (a) the sum of the points is 2; (b) the sum of the points is 10; (c) the sum of the points is at least 10; (d) the point 6 occurs at least once.
A coin is tossed five times in succession, and the event is: (a) obtaining more heads than tails; (b) obtaining two heads; (c) obtaining at least one head; (d) obtaining at most one head; (e) the difference between numbers of heads and tails is unity.
2. What is the role of effect size in a meta-analysis?
1. What is meta-analysis?
5. What are the effect size conventions?
4. On a standard test, the population is known to have a mean of 500 and a standard deviation of 100. Those receiving an experimental treatment have a mean of 540. What is the effect size?
3. Write the formula for effect size in the situation we have been considering.
2. Why do researchers usually use a standardized effect size?
1. What does effect size add to just knowing whether a result is significant?
5. Decide whether to reject the null hypothesis. The Z score of the sample’s mean is −2.50, which is more extreme than −1.96; reject the null hypothesis. Seeing the video does change attitudes toward alcohol.
4. Determine your sample’s score on the comparison distribution. Z=(M−Population MM)/Population SDM=(70−75)/2=−2.50.
3. Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. Two-tailed cutoffs, 5% significance level, are +1.96 and −1.96.
2. Determine the characteristics of the comparison distribution.Population MM=Population M=75. Population SDM2=Population S
21. A government-sponsored telephone counseling service for adolescents tested whether the length of calls would be affected by a special telephone system that had a better sound quality. Over the past several years, the lengths of telephone calls (in minutes) were normally distributed with
20. A researcher is interested in the conditions that affect the number of dreams per month that people report in which they are alone. We will assume that based on extensive previous research, it is known that in the general population the number of such dreams per month follows a normal curve,
19. A researcher is interested in whether people are able to identify emotions correctly in other people when they are extremely tired. It is known that, using a particular method of measurement, the accuracy ratings of people in the general population (who are not extremely tired)are normally
18. ADVANCED TOPIC: Figure the 99% confidence interval (that is, the lower and upper confidence limits) for each part of problem 14. Assume that in each case the researcher’s sample has a mean of 50 and that the population of individuals is known to follow a normal curve.
17. ADVANCED TOPIC: Figure the 95% confidence interval (that is, the lower and upper confidence limits) for each part of problem 13. Assume that in each case the researcher’s sample has a mean of 80 and the population of individuals is known to follow a normal curve.
16. For each of the following studies, the samples were given an experimental treatment and the researchers compared their results to the general population. (Assume all populations are normally distributed.)For each, carry out a Z test using the five steps of hypothesis testing for a two-tailed
15. For each of the studies shown below, the samples were given an experimental treatment and the researchers compared their results to the general population. (Assume all populations are normally distributed.)For each, carry out a Z test using the five steps of hypothesis testing for a two-tailed
14. Figure the standard deviation of the distribution of means for a population with a standard deviation of 20 and sample sizes of (a) 10,(b) 11, (c) 100, and (d) 101.
13. Indicate the mean and the standard deviation of the distribution of means for each of the situations shown here.Population Sample Size Situation M SD2 N(a) 100 40 10(b) 100 30 10(c) 100 20 10(d) 100 10 10(e) 50 10 10(f) 100 40 20(g) 100 10 20 6.1-2 Full Alternative Text
12. Under what conditions is it reasonable to assume that a distribution of means will follow a normal curve?
11. ADVANCED TOPIC: Christakis and Fowler (2007) studied more than 12,000 people over a 32-year period to examine if people’s chances of becoming obese are related to whether they have friends and family who become obese. They reported that “A person’s chance of becoming obese increased by
10. Marczinski and colleagues (2012) randomly assigned participants to consume one of four drinks: an alcoholic drink, an energy drink, a drink containing alcohol mixed with energy drink (AmED), or a decaffeinated soda (which was the control or “placebo” drink). The participants then completed
9. A large number of people were shown a video of an automobile collision between a moving car and a stopped car. Each person then filled out a questionnaire about how likely it was that the driver of the moving car was at fault, on a scale from 0=not at fault to 10=completely at fault. The
8. Twenty-five women between the ages of 70 and 80 were randomly selected from the general population of women take part in a special program to decrease response time (speed it took them) to answer a particular kind of question. After the course, the women had an average response time of 1.5
7. For each of the following samples that were given an experimental treatment, test whether they represent populations that score significantly higher than the general population: (a) a sample of 100 with a mean of 82 and (b) a sample of 10 with a mean of 84. The general population of individuals
6. For each of the following samples that were given an experimental treatment, test whether these samples represent populations that are different from the general population: (a) a sample of 10 with a mean of 44 and (b) a sample of 1 with a mean of 48. The general population of individuals has a
5. ADVANCED TOPIC: Figure the 99% confidence interval (that is, the lower and upper confidence limits) for each part of problem 3. Assume that in each case the researcher’s sample has a mean of 10 and that the population of individuals is known to follow a normal curve.
4. ADVANCED TOPIC: Figure the 95% confidence interval (that is, the lower and upper confidence limits) for each part of problem 2. Assume that in each case the researcher’s sample has a mean of 100 and that the population of individuals is known to follow a normal curve.
3. For a population that has a standard deviation of 20, figure the standard deviation of the distribution of means for samples of size (a) 2, (b) 3, (c)4, and (d) 9.
2. For a population that has a standard deviation of 10, figure the standard deviation of the distribution of means for samples of size (a) 2, (b) 3, (c)4, and (d) 9.
1. Why is the standard deviation of the distribution of means generally smaller than the standard deviation of the distribution of the population of individuals?
4. Describe how to change the Z scores to raw scores to find the confidence interval.
3. Mention that you next find the Z scores that go with the confidence interval that you want.
2. Explain that the first step in figuring a confidence interval is to estimate the mean of the population represented by the sample studied (for which the best estimate is the sample mean) and figure the standard deviation of the distribution of means.
1. Explain that a confidence interval is an estimate (based on your sample’s mean and the standard deviation of the distribution of means) of the range of values that are likely to include the true population mean for the group studied (Population 1). Be sure to mention that the 95% (or
3. To find the confidence interval, change these Z scores to raw scores.Lower confidence limit=(−2.58)(.57)+16=−1.47+16=14.53; upper confidence limit=(2.58)(.57) +16=17.47. The 99% confidence interval is from 14.53 to 17.47
2. Find the Z scores that go with the confidence interval you want. For the 99% confidence interval, the Z scores are +2.58 and −2.58.
1. Estimate the mean of the population represented by our sample and figure the standard deviation of the distribution of means. The best estimate of the mean of the population represented by our sample in the preceding problem is the sample mean of 16. The standard deviation of the distribution of
5. Explain how and why the scores from Steps and of the hypothesis-testing process are compared. Explain the meaning of the result of this comparison with regard to the specific research and null hypotheses being tested.
4. Describe why and how you figure the Z score of the sample mean on the comparison distribution.
3. Describe the logic and process for determining (using the normal curve)the cutoff sample score(s) on the comparison distribution at which the null hypothesis should be rejected.
2. Explain the concept of the comparison distribution. Be sure to mention that with a sample of more than one, the comparison distribution is a distribution of means because the information from the study is a mean of a sample. Mention that the distribution of means has the same mean as the
1. Describe the core logic of hypothesis testing in this situation. Be sure to explain the meaning of the research hypothesis and the null hypothesis in this situation where we focus on the mean of a sample and compare it to a known population mean. Explain the concept of support being provided for
4. A researcher predicts that showing a certain video will change people’s attitudes toward alcohol. The researcher then randomly selects 36 people, shows them the video, and gives them an attitude questionnaire.The mean score on the attitude test for these 36 people is 70. The score on this test
3. What is a 95% confidence interval?
2. (a) What number is used to indicate the accuracy of an estimate of the population mean? (b) Why?
1. (a) What is the best estimate of a population mean? (b) Why?
3. A researcher predicts that showing a certain video will change people’s attitudes toward alcohol. The researcher then randomly selects 36 people, shows them the video, and gives them an attitude questionnaire.The mean score on the attitude test for these 36 people is 70. The score for people
2. How do you find the Z score for the sample’s mean on the distribution of means?
1. What is the main way in which hypothesis testing with a sample of more than one person is different from hypothesis testing with a sample of a single person?
4. Describe how to change the Z scores to raw scores to find the confidence interval.
3. Mention that you next find the Z scores that go with the confidence interval that you want.
2. Explain that the first step in figuring a confidence interval is to estimate the mean of the population represented by the sample studied (for which the best estimate is the sample mean) and figure the standard deviation of the distribution of means.
1. Explain that a confidence interval is an estimate (based on your sample’s mean and the standard deviation of the distribution of means) of the range of values that are likely to include the true population mean for the group studied (Population 1). Be sure to mention that the 95% (or
2. Find the Z scores that go with the confidence interval you want. For the 99% confidence interval, the Z scores are +2.58 and −2.58.3. To find the confidence interval, change these Z scores to raw scores.Lower confidence limit=(−2.58)(.57)+16=−1.47+16=14.53; upper confidence
1. Estimate the mean of the population represented by our sample and figure the standard deviation of the distribution of means. The best estimate of the mean of the population represented by our sample in the preceding problem is the sample mean of 16. The standard deviation of the distribution of
5. Explain how and why the scores from Steps and of the hypothesis-testing process are compared. Explain the meaning of the result of this comparison with regard to the specific research and null hypotheses being tested.
4. Describe why and how you figure the Z score of the sample mean on the comparison distribution.
3. Describe the logic and process for determining (using the normal curve)the cutoff sample score(s) on the comparison distribution at which the null hypothesis should be rejected.
2. Explain the concept of the comparison distribution. Be sure to mention that with a sample of more than one, the comparison distribution is a distribution of means because the information from the study is a mean of a sample. Mention that the distribution of means has the same mean as the
1. Describe the core logic of hypothesis testing in this situation. Be sure to explain the meaning of the research hypothesis and the null hypothesis in this situation where we focus on the mean of a sample and compare it to a known population mean. Explain the concept of support being provided for
5. Decide whether to reject the null hypothesis. The sample’s Z score of 1.75 is not more extreme than the cutoffs of +1.96 and −1.96; do not reject the null hypothesis. The results are inconclusive. The distributions involved are shown in Figure 6–10
4. Determine your sample’s score on the comparison distribution. Using the formula Z=(M−Population MM)/Population SDM, Z=(16−15)/.57=1/.57=1.75.
3. Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. Two-tailed cutoffs, .05 significance level, are +1.96 and −1.96.
2. Determine the characteristics of the comparison distribution. Population MM= Population M=15. Population SDM2= Population SD2/N=52/75=.33 Population SDM=Population SDM2=.33=.57; shape is roughly normal(sample size is greater than 30).
1. Restate the question as a research hypothesis and a null hypothesis about the populations. The two populations are:Population 1: Those given the experimental treatment.Population 2: People in the general population (who are not given the experimental treatment).The research hypothesis is that
4. A researcher predicts that showing a certain video will change people’s attitudes toward alcohol. The researcher then randomly selects 36 people, shows them the video, and gives them an attitude questionnaire.The mean score on the attitude test for these 36 people is 70. The score on this test
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