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statistics for engineers and scientists
Statistics For The Behavioral And Social Sciences A Brief Course 6th Edition Arthur Aron Elliot J Blows Elaine N Aron - Solutions
2. (a) What number is used to indicate the accuracy of an estimate of the population mean? (b) Why?3. What is a 95% confidence interval?
1. (a) What is the best estimate of a population mean? (b) Why?
3. Change these Z scores to raw scores to find the confidence interval. To find the lower limit, multiply −1.96 (for the 95% confidence interval) or−2.58 (for the 99% confidence interval) by the standard deviation of the distribution of means (Population SDM) and add this to the population
2. Find the Z scores that go with the confidence interval you want. For the 95% confidence interval, the Z scores are +1.96 and −1.96. 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 population mean for the population represented by your sample is the sample mean. Next, find the variance of the distribution of means in the
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?
6. A population of individuals has a normal distribution, a mean of 60, and a standard deviation of 10. What are the characteristics of a distribution of means from this population for samples of four each?
5. (a) What is the standard error (SE)? (b) Why does it have this name?
4. Write the formula for the variance of the distribution of means, and define each of the symbols.
3. (a) Why is the mean of the distribution of means the same as the mean of the population of individuals? (b) Why is the variance of a distribution of means smaller than the variance of the distribution of the population of individuals?
2. Explain how you could create a distribution of means by taking a large number of samples of four individuals each.
1. What is a distribution of means?
21. McConnell and colleagues (2011) conducted several studies to examine whether people who own pets differ from those who don’t in terms of their well-being, personality, and attachment styles (their expectations about close relationships). Table 5–5 shows the results of one of their studies.
20. Gentile (2009) conducted a survey study of video-game use in a random sample of 1,178 American youth aged 8–18 years. In his results section, Gentile reported, “[T]here was a sizable difference between boys’average playing time [of video games] (M=16.4hr/week, SD=14.1) and girls’
19. A researcher predicts that listening to classical music while solving math problems will make a particular brain area more active (this is a fictional study). To test this, a research participant has her brain scanned while listening to classical music and solving math problems, and the brain
18. A researcher developed a new training program to reduce the stress of childless men who marry women with adolescent children (this is a fictional study). It is known from previous research that such men, one month after moving in with their new wife and her children, have a stress level of 85
17. A researcher wants to test whether a certain sound will make rats do worse on learning tasks (this is a fictional study). It is known that an ordinary rat can learn to run a particular maze correctly in 18 trials, with a standard deviation of 6. (The number of trials to learn this maze is
16. Based on the information given for each of the following studies, decide whether to reject the null hypothesis. For each, give (a) the Z-score cutoff (or cutoffs) on the comparison distribution at which the null hypothesis should be rejected, (b) the Z score on the comparison distribution for
15. Based on the information given for each of the following studies, decide whether to reject the null hypothesis. For each, give (a) the Z-score cutoff (or cutoffs) on the comparison distribution at which the null hypothesis should be rejected, (b) the Z score on the comparison distribution for
3. Do people who live in big cities develop more stress-related conditions than people in general?
2. Based on anthropological reports in which the status of women is scored on a 10-point scale, the mean and standard deviation across many cultures are known. A new culture is found in which there is an unusual family arrangement. The status of women is also rated in this culture. Do cultures with
1. In an experiment, people are told to solve a problem by focusing on the details. Is the speed of solving the problem different for people who get such instructions compared to the speed for people who are given no special instructions?
10. For each of the following studies, make a chart of the four possible correct and incorrect decisions, and explain what each would mean.Each chart should be laid out like Table 5–3, but you should put into the boxes the possible results, using the names of the variables involved in the
9. Stoet, O’Connor, Conner, and Laws (2013) conducted several experiments to examine the multitasking skills of men and women. In one experiment, the participants spent 8 minutes attempting three tasks.The results are shown in Table 5–4. Focusing on just the means and p value in the first line
8. Robins and John (1997) carried out a study on narcissism (extreme selflove), comparing people who scored high versus low on a narcissism questionnaire. (An example item was “If I ruled the world, it would be a better place.”) They also had other questionnaires, including one that had an item
7. A nursing researcher is working with people who have had a particular type of major surgery. This researcher proposes that people will recover from the operation more quickly if friends and family are in the room with them for the first 48 hours after the operation (this is a fictional study).
6. A researcher studying the senses of taste and smell has carried out many studies in which students are given each of 20 different foods by dropping a liquid on the tongue (apricot, chocolate, cherry, coffee, garlic, etc.) (this is a fictional study). Based on her past research, she knows that
5. Based on the information given for each of the following studies, decide whether to reject the null hypothesis. For each, give (a) the Z-score cutoff (or cutoffs) on the comparison distribution at which the null hypothesis should be rejected, (b) the Z score on the comparison distribution for
4. Based on the information given for each of the following studies, decide whether to reject the null hypothesis. For each, give (a) the Z-score cutoff (or cutoffs) on the comparison distribution at which the null hypothesis should be rejected, (b) the Z score on the comparison distribution for
3. Do people who have just experienced their grandmother’s 90th birthday have more or less self-confidence than the general population?
2. Is the level of income for residents of a particular city different from the level of income for people in the region?
1. Do Canadian children whose parents are librarians score higher than Canadian children in general on reading ability?
3. For each of the following, (a) say which two populations are being compared, (b) state the research hypothesis, (c) state the null hypothesis, and (d) say whether you should use a one-tailed or two-tailed test and why.
2. When a result is not extreme enough to reject the null hypothesis, explain why it is wrong to conclude that your result supports the null hypothesis.
1. Define the following terms in your own words: (a) hypothesis-testing procedure, (b) .05 significance level, and (c) two-tailed test.
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 how to figure the sample’s score on the comparison distribution.
3. Describe the logic and process for determining (using the normal curve)the cutoff sample scores on the comparison distribution at which you should reject the null hypothesis.
2. Explain the concept of the comparison distribution. Be sure to mention that it is the distribution that represents the population situation if the null hypothesis is true. Note that the key characteristics of the comparison distribution are its mean, standard deviation, and shape.
1. Describe the core logic of hypothesis testing. Be sure to explain terminology such as research hypothesis and null hypothesis, and explain the concept of providing support for the research hypothesis when the study results are strong enough to reject the null hypothesis.
5. Decide whether to reject the null hypothesis. A Z score of 2 is more extreme than the cutoff Z of ±1.96. Reject the null hypothesis; the result is significant. The evidence supports the conclusion that the experimental treatment affects scores on this measure. The diagram is shown in Figure
4. Determine your sample’s score on the comparison distribution. Z=(X−M)/SD=(27−19)/4=2.
3. Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. For a two-tailed test at the 5% level (2.5% at each tail), the cutoff sample scores are +1.96 and−1.96 (see Figure 5–4 or Table 5–2).
2. Determine the characteristics of the comparison distribution: Population M=19, Population SD=4, normally distributed.
1. Restate the question as a research hypothesis and a null hypothesis about the populations. There are two populations of interest:Population 1: People who go through the experimental treatment.Population 2: People in general (that is, people who do not go through the experimental treatment).The
5. Decide whether to reject the null hypothesis.
4. Determine your sample’s score on the comparison distribution.
3. Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected.
2. Determine the characteristics of the comparison distribution.
1. Restate the question as a research hypothesis and a null hypothesis about the populations.
5. If you set an extreme significance level (say, .001), what is the effect on the probability of (a) Type I error and (b) Type II error?
4. If you set a lenient significance level (say, .25), what is the effect on the probability of (a) Type I error and (b) Type II error?
3. (a) What is a Type II error? (b) Why is it possible?
2. (a) What is a Type I error? (b) Why is it possible? (c) What is its probability?
1. What is a decision error?
6. A researcher predicts that making people hungry will affect how they do on a coordination test. A randomly selected person is asked not to eat for 24 hours before taking a standard coordination test and gets a score of 600. For people in general of this age group and gender, tested under normal
5. Why might you use a two-tailed test even when your theory predicts a particular direction of result?
4. What is the advantage of using a one-tailed test when your theory predicts a particular direction of result?
3. Why do you use a two-tailed test when testing a nondirectional hypothesis?
2. What is a two-tailed test?
1. What is a nondirectional hypothesis test?
5. Decide whether to reject the null hypothesis. A Z score of −2.45 is more extreme than the Z score of −1.96, which is where the lower 2.5% of the comparison distribution begins. Notice in Figure 5–5 that the Z score of−2.45 falls within the shaded area in the left tail of the comparison
4. Determine your sample’s score on the comparison distribution. The police chief whose city went through the earthquake took the standard attitude questionnaire and had a score of 35. This corresponds to a Z score on the comparison distribution of −2.45. That is,
3. Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. The researcher selects the 5% significance level. The researcher has made a nondirectional hypothesis and will therefore use a two-tailed test. Thus, the researcher will reject the
2. Determine the characteristics of the comparison distribution. If the null hypothesis is true, the distributions of Populations 1 and 2 are the same.We know the distribution of Population 2, so we can use it as our comparison distribution. As noted, it follows a normal curve, with Population
7. How is it possible that a result can be statistically significant but be of little practical importance?
6. A training program to increase friendliness is tried on one individual randomly selected from the general public. Among the general public(who do not get this training program), the mean on the friendliness measure is 30 with a standard deviation of 4. The researchers want to test their
5. What can you conclude when (a) a result is so extreme that you reject the null hypothesis, and (b) a result is not very extreme so that you cannot reject the null hypothesis?
4. Why do we say that hypothesis testing involves a double negative logic?
3. What is the cutoff sample score?
. (a) What is a comparison distribution? (b) What role does it play in hypothesis testing?
1. A sample of rats in a laboratory is given an experimental treatment intended to make them learn a maze faster than other rats. State (a) the null hypothesis and (b) the research hypothesis.
5. Decide whether to reject the null hypothesis.
4. Determine your sample’s score on the comparison distribution.
3. Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected.
2. Determine the characteristics of the comparison distribution.
1. Restate the question as a research hypothesis and a null hypothesis about the populations.
24. You apply to 20 graduate programs, 5 of which are in New Zealand, 5 of which are in Canada, and 10 of which are in the United States. You get a text from home that you have a letter from one of the programs to which you applied, but nothing is said about which one. Give the probability it is
23. You are conducting a survey at a university with 800 students, 50 faculty members, and 150 administrators. Each of these 1,000 individuals has a single listing in the campus email directory. Suppose you were to select one email address at random. What is the probability it would be the email
22. Suppose that you were going to conduct a survey of visitors to your campus. You want the survey to be as representative as possible. (a)How would you select the people to survey? (b) Why would that be your best method?
21. Felix and Afifi (2015) conducted a study to examine the mental health and stress experiences of people living in several communities in California that had experienced highly destructive wildfires. In the methods section of their article, the researchers noted that: “Random digit dial
20. Suppose you want to conduct a survey of the voting preference of undergraduate students. One approach would be to contact every undergraduate student you know and ask them to fill out a questionnaire.(a) What kind of sampling method is this? (b) What is a major limitation of this kind of
19. Suppose that you are designing an instrument panel for a large industrial machine. The machine requires the person using it to reach 2 feet from a particular position. The reach from this position for adult women is known to have a mean of 2.8 feet with a standard deviation of .5. The reach for
18. In the example in problem 16, assume that the mean is 300 and the standard deviation is 25. Using a normal curve table, what scores would be the top and bottom score to find (a) the middle 50% of architects, (b)the middle 90% of architects, and (c) the middle 99% of architects?
17. In the example in problem 16, using a normal curve table, what is the minimum Z score an architect can have on the creativity test to be in the(a) top 50%, (b) top 40%, (c) top 60%, (d) top 30%, and (e) top 20%?
16. Suppose that the scores of architects on a particular creativity test are normally distributed. Using a normal curve table, what percentage of architects have Z scores (a) above .10, (b) below .10, (c) above .20, (d)below .20, (e) above 1.10, (f) below 1.10, (g) above −.10, and (h)
15. Using the information in problem 14 and the 50%–34%–14% figures, what is the longest time to complete the word puzzle a person can have and still be in the bottom (a) 2%, (b) 16%, (c) 50%, (d) 84%, and (e)98%?
14. The length of time it takes to complete a word puzzle is found to be normally distributed with a mean of 80 seconds and a standard deviation of 10 seconds. Using the 50%–34%–14% figures, approximately what percentage of scores (on time to complete the word puzzle) will be (a)above 100, (b)
13. Consider a test that has a normal distribution, a mean of 100, and a standard deviation of 14. How high a score would a person need to be in(a) the top 1% and (b) the top 5%?
12. The following numbers of employees in a company received special assistance from the personnel department last year:Drug/alcohol 10 Family crisis counseling 20 Other 20 Total 50¯4.1-2 Full Alternative Text If you were to select a score at random from the records for last year, what is the
11. Barnes and colleagues (2015) conducted a telephone survey of gambling and substance use behaviors (such as smoking and alcohol use) among U.S. adults. They explained that “the co-occurrence between problem gambling and substance abuse is studied using a large-scale, representative sample of
10. A research article is concerned with the level of self-esteem of Australian high school students. The methods section emphasizes that a“random sample” of Australian high school students was surveyed.Explain to a person who has never had a course in statistics what this means and why it is
9. Consider a test of coordination that has a normal distribution, a mean of 50, and a standard deviation of 10. (a) How high a score would a person need to be in the top 5%? (b) Explain your answer to someone who has never had a course in statistics.
8. Assuming a normal curve, (a) if a person is in the top 10% of his or her country on mathematics ability, what is the lowest Z score this person could have? (b) If the person is in the top 1%, what would be the lowest Z score this person could have?
7. Assuming a normal curve, (a) if a student is in the bottom 30% of the class on Spanish ability, what is the highest Z score this person could have? (b) If the person is in the bottom 3%, what would be the highest Z score this person could have?
6. Using a normal curve table, give the percentage of scores between the mean and a Z score of (a) .58, (b) .59, (c) 1.46, (d) 1.56, and (e) −.58.
5. In the test anxiety example of problems 3 and 4, using a normal curve table, what is the lowest score on the test anxiety measure a person has to have to be in (a) the top 40%, (b) the top 30%, and (c) the top 20%?
4. In the previous problem, the measure of test anxiety has a mean of 15 and a standard deviation of 5. Using a normal curve table, what percentage of students have scores (a) above 16, (b) above 17, (c) above 18, (d) below 18, and (e) below 14?
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