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Mind On Statistics 4th Edition David D Busch, Jessica M Utts, Robert F Heckard - Solutions

Refer to Exercise 14.7. Suppose a woman is 63 inches tall and her desired weight is 115 pounds. Give numerical values for each of the following for this individual:a. x.b. y.c. y^.d. The residual.e. The component of y that is explained by knowing x.f. The unexplained part of y
Heights and answers to the question, “How much would you like to weigh?” were recorded for n 5 126 women in a statistics class. A regression equation for y 5 desired weight(in pounds) and x 5 height (in inches) is Estimated mean desired weight 5 265.4 1 2.90 (Height)(Data source: William
The linear relationship between the number of bedrooms a house has and the selling price of the house (in dollars) is analyzed for a sample of n 5 250 recently sold houses in a large metropolitan area. The sample regression line is Predicted selling price 5 144000 1 50000 (Bedrooms)a. Give the
Suppose that medical researchers use sample data to find a regression line describing the relationship between y 5 systolic blood pressure and x 5 age for men between 40 and 60 years old and that the sample regression line is Estimated mean systolic blood pressure 5 85 1 0.9(Age)a. Give the value
Ages of husbands and wives are recorded for a randomly selected sample of n 5 200 opposite-sex married couples
The population model for simple linear regression can be defined as yi 5 b0 1 b1xi 1 eia. Explain what the parameters b0 and b1 represent.b. Write the equation that represents how the mean of the y variable relates to the x variable.
For each of the following, specify whether the notation or word applies to the population or the sample. If it applies to the population, give the notation or word for the corresponding feature in the sample, and if it applies to the sample, give the notation or word for the corresponding feature
◆ The temperature dataset on the companion website gives y 5 mean April temperature (Fahrenheit) and x 5 geographic latitude for 20 U.S. cities. The simple linear regression equation for the sample is y^ 5 119 2 1.64x.a. The value of latitude for Pittsburgh is 40. What is the predicted April
The dataset deprived includes information on self-reported amount of sleep per night and whether a person feels sleepdeprived for n 5 86 college students (Source: Laura Simon, Pennsylvania State University). Assume that the students represent a random sample of college students. Is the mean number
The dataset UCDavis2 includes grade point average GPA and answers to the question: “Where do you typically sit in a classroom (circle one): Front, Middle, Back.” The answer to this question is coded as F, M, B for the variable Seat. Assuming these students represent all college students, test
The dataset UCDavis2 includes information on Sex, Height, and Dadheight. Use the data to test the hypothesis that college men are taller, on average, than their fathers. Assume that the male students in the survey represent a random sample of college men.
Refer to Exercises 13.110 and 13.111. Using the dataset cholest, determine whether there is sufficient evidence to conclude that the cholesterol level drops, on average, from day 2 to day 14 after a heart attack.
Refer to Exercise 13.110. Suppose that physicians will use the answer to that question to decide whether to retest patients’ cholesterol levels on day 4. If there is no conclusive evidence that the cholesterol level goes down, they will use the day 2 level to decide whether to prescribe drugs for
◆ The dataset cholest on the companion website reports cholesterol levels of heart attack patients 2, 4, and 14 days after the heart attack. Data for days 2 and 4 were available for 28 patients. The mean difference (2 day 2 4 day) was 23.29, and the standard deviation of the differences was
Refer to Case Study 13.1. The mean and standard deviation for the 10 differences in times to exhaustion after drinking a slushie and drinking cold water were d 5 9.5 minutes and sd 5 3.6 minutes.a. Compute a two-sided 95% confidence interval for the population mean difference.b. Use the interval
Refer to Exercise 13.107. The experiment was repeated in 2010 using updated population figures of 308 million for the United States and 22 million for Australia when the questions were asked. At the time, the population of Canada was about 34 million. Here are the summary statistics for the results:
In an experiment conducted by one of the authors, ten students in a graduate-level statistics course were given this question about the population of Canada: “The population of the U.S. is about 270 million. To the nearest million, what do you think is the population of Canada?” (The population
It is believed that regular physical exercise leads to a lower resting pulse rate. Following are data for n 5 20 individuals on resting pulse rate and whether the individual regularly exercises or not. Assuming that this is a random sample from a larger population, use this sample to determine if
had not.)Specify the value of a that you must use given the available information.
Refer to Exercise 13.104. One of the statements made in the research article and reported in Exercise 11.82 was “After control for confounding background variables ... the average difference observed at 36 and 48 months was reduced to 4.35 points (95% CI: 0.02, 8.68).” Use this statement to
In Exercise 11.82, a study is described in which the mean IQs at age 4 for children of smokers (at least ten cigarettes a day)and nonsmokers were compared. The mean for the children of the 66 nonsmokers was 113.28 points, while for the children of the 47 smokers it was 103.12 points. Assume that
This is Thought Question 13.4. Refer to Example 13.9. A 95%confidence interval for the difference in proportions of children who would get ear infections with placebo compared to with xylitol was 0.02 to 0.226. On the basis of this information, specify a one-sided 97.5% confidence interval and
Suppose that a highway safety researcher makes modifications to the design of a highway sign. The researcher believes that the modifications will make the mean maximum distance at which drivers are able to read the sign greater than 450 feet. The maximum distances (in feet) at which n 5 16 drivers
In a random sample of 170 married British couples, the difference between the husband’s and wife’s ages had a mean of 2.24 years and a standard deviation of 4.1 years.a. Test the hypothesis that British men are significantly older than their wives, on average. Specify the value of a that you
This exercise is Thought Question 13.3. The paired t-test introduced in Section 13.3 and the two-sample t-test introduced in Section 13.4 are both used to compare two sets of measurements, and the null hypothesis in both cases is usually that the mean population difference is 0.a. Explain the
Suppose that a one-sample t-test of H0: m 5 0 versus Ha: m 2 0 results in a test statistic of t 5 0.65 with df 5 14. Suppose that a new study is done with n 5 150, and the sample mean and standard deviation turn out to be exactly the same as in the first study.a. What conclusion would you reach in
A study is conducted to find out whether results of an IQ test are significantly higher after listening to Mozart than after sitting in silence. Explain what has happened in each of the following scenarios:a. A Type 1 error was committed.b. A Type 2 error was committed.c. The power of the test was
Refer to Exercise 13.96. In each case, specify whether the alternative hypothesis would be one-sided or two-sided.
For each of the following research questions, specify the parameter and the value that constitute the null hypothesis of “parameter 5 null value.” In other words, define the population parameter of interest and specify the null value that is being tested.a. Do a majority of Americans between
Answer the following questions about the study reported as Case Study 13.1. Explain your answers.a. Was the study a randomized experiment or an observational study?b. Based on your answer in part (a), can it be concluded that drinking an ice slushie before exercising in the heat causes time to
Using the Bonferroni method, what significance level should be used for each individual test in each of the following situations?a. Overall significance level is .10 and five tests are to be conducted.b. Overall significance level is .05 and two tests are to be conducted.
This is also Exercise 1.19. A (hypothetical) study of what people do in their spare time found that people born under the astrological sign of Aries were significantly more likely to be regular swimmers than people born under other signs. What additional information would you want to know to help
This is also Exercise 1.42b. Suppose that you were to read the following news story: “Researchers compared a new drug to a placebo for treating high blood pressure, and it seemed to work. But the researchers were concerned because they found that significantly more people got headaches when
Refer to the checklist of issues on pp. 531–532.a. For which of the concerns would the p-value for a test be useful to have? Explain why in each case.b. For which of the concerns would a confidence interval estimate for the parameter be useful to have? Explain why in each case.c. For which of the
Refer to the statement in Item 6 in the checklist of issues on pp. 531–532 that begins with “Remember that if all of the null hypotheses tested....” Is that statement the same thing as saying that the null hypothesis is likely to be true in about 1 out of 20 tests that have achieved
Refer to the checklist of issues on pp. 531–532. Explain which ones should be of concern if the sample size(s) for a test are large.
Refer to the checklist of issues on pp. 531–532. Explain which ones should be of concern if the sample size(s) for a test are small.
Refer to the effect-size measure in Exercise 13.86. For parts(a) to (c), compute the effect size.a. p 5 .35, p0 5 .25.b. p 5 .15, p0 5 .05.c. p 5 .95, p0 5 .85.d. On the basis of the results in parts (a) to (c), does this effect size stay the same when p 2 p0 stays the same?Explain.e. In
For a z-test for one proportion, a possible effect size measure is 1p 2 p02/"p0 11 2 p02 where p0 is the null value and p is the true population proportion, which can be estimated using the sample proportion.a. What is the relationship between this effect size and the z-test statistic for this
Explain why it is more useful to compare effect sizes than p-values in trying to determine whether many studies about the same topic have found similar results.
Refer to Figure 13.9 on page 530, showing power curves for a one-sided t-test. Use the Figure to answer the following questions for a one-sided t-test with a 5 .05. Explain your answers.a. If the true effect size is 0.3, would a sample of size n 5 20 be large enough to achieve power of at least
on page 530, showing power curves for a one-sided t-test. Use the Figure to give the approximate power in each of the following situations, and write a sentence explaining what probability is represented by the power.a. n 5 20, true effect size 5 0.4.b. n 5 50, true effect size 5 0.4.c. n 5 100,
Refer to Figure
(Computer software is required.) In parts (a) to (d), find the sample size necessary to achieve power of .80 for a onesample t-test with Ha: m . m0 and level of significance of .05 for each of the following effect sizes:a. 0.2.b. 0.4.c. 0.6.d. 0.8.e. Make a scatterplot of the sample size (vertical
(Computer software is required.) Find the power for the following one-sample t-test situations. In each case, assume that a .05 level of significance will be used.a. Effect size 5 0.3, sample size 5 45, Ha: m . m0.b. Sample size 5 30, Ha: m 2 10, true mean 5 13, s 5 4.c. Effect size 5 21.0, sample
In Table 13.4 (p. 530), it is shown that the power is .40 for a one-sided, one-sample t-test with .05 level of significance, n 5 50, and true effect size of 0.2. Would the power be higher or lower for each of the following changes?a. The true effect size is 0.4.b. The sample size used is n 5 75.c.
Refer to Table 13.4 (p. 530), which presents power for a onesided, one-sample t-test. In a test of H0: md 5 0 versus Ha: md . 0, suppose that the truth is that the population of differences is a normal distribution with mean md 5 2 and standard deviation s 5 4.a. Recalling the Empirical Rule from
Compute the effect size for each of the following situations, and state whether it would be considered closer to a small, medium, or large effect:a. In a paired-difference test with n 5 30 pairs, the test statistic is t 5 1.48.b. In a test for the difference in two means with independent samples,
Compute the effect size for each of the following situations, and state whether it would be considered closer to a small, medium, or large effect:a. In a one-sample test with n 5 100, the test statistic is t 5 2.24.
Refer to the following two scenarios from exercises in various chapters of this book. In each case, determine the most appropriate inference procedure(s), including the appropriate parameter. If you think that inference about more than one parameter may be of interest, answer the question for all
Refer to the following two scenarios from exercises in various chapters of this book. In each case, determine the most appropriate inference procedure(s), including the appropriate parameter. If you think that inference about more than one parameter may be of interest, answer the question for all
Give an example of a situation for which the appropriate inference procedure would be each of the following:a. A hypothesis test for one proportion.b. A hypothesis test and confidence interval for a paired difference mean.c. A confidence interval for one mean.d. A confidence interval for the
(p. 524)is or are appropriate for this situation? Give the parameter(s) in symbols, and define what the symbol(s) represent in the context of the situation.
Researchers want to compare the mean running times for the 50-yard dash for first-grade boys and girls. They select a random sample of 35 boys and 32 girls in first grade and time them running the 50-yard dash.a. Which of the five parameters given in Table
Refer to Exercise 13.71. Researchers also want to compare the average number of visits made by adults who fear going to the dentist with the average number of visits for those who don’t have the fear.a. Which of the five parameters given in Table 13.3 (p. 524)is or are appropriate for this
Researchers want to know what percentage of adults have a fear of going to the dentist. They also want to know the average number of visits made to a dentist in the past 10 years for adults who have that fear. They ask a random sample of adults whether or not they fear going to the dentist and also
Researchers want to know what proportion of a certain type of tree growing in a national forest suffers from a disease. They test a representative sample of 200 of the trees from around the forest and find that 15 of them have the disease.a. Which of the five parameters given in Table 13.3 (p.
For each of the following situations, can you conclude whether a two-sided 90% confidence interval for m would include the value 10? If so, make the conclusion. If not, explain why you can’t tell.a. H0: m 5 10, Ha: m , 10, do not reject the null hypothesis for a 5 .05.b. H0: m 5 10, Ha: m , 10,
As was stated in Section 13.5, “a confidence interval can be used as another way to conduct a two-sided significance test.” If a test were conducted by using this method, would the p-value for the test be available? Explain.
Each of the following presents a two-sided 95% confidence interval and the alternative hypothesis of a corresponding hypothesis test. In each case, state a conclusion for the test, including the level of significance you are using.a. C.I. for m is (101 to 105), Ha: m 2 100.b. C.I. for p is (.12 to
Refer to the rules for the relationship between confidence intervals and one-sided tests given in the three bullets and sentence preceding them on page 522.a. Rewrite the rules specifically for a 5 .05.b. Rewrite the rules specifically for a 5 .01.
Refer to the rules for the relationship between confidence intervals and tests with two-sided alternatives, given in the two bullets on page 521.a. Rewrite the rules specifically for a 5 .05.b. Rewrite the rules specifically for a 5 .01.
In each of the following cases, explain whether the null hypothesis H0: m 5 25 can be rejected. Use a 5 .05.a. 95% confidence interval for m is (26 to 50), Ha: m 2 25.b. 90% confidence interval for m is (10 to 30), Ha: m , 25.c. 90% confidence interval for m is (26 to 50), Ha: m , 25.
In each of the following cases, explain whether the null hypothesis H0: m 5 25 can be rejected. Use a 5 .05.a. 95% confidence interval for m is (10 to 30), Ha: m 2 25.b. 90% confidence interval for m is (10 to 30), Ha: m . 25.c. 90% confidence interval for m is (26 to 50), Ha: m . 25.
In Example 11.12 (p. 428) a study by Slutske, Piasecki, and Hunt-Carter (2003; and on the website for this book) was presented, in which the mean number of hangover symptoms was compared for students whose parents have alcohol problems and students whose parents do not. Researchers are interested
Researchers speculate that drivers who do not wear a seatbelt are more likely to speed than drivers who do wear one.The following data were collected on a random sample of 20 drivers who were clocked to see how fast they were driving(miles per hour), and then were stopped to see whether they were
Students in a statistics class at Penn State were asked,“About how many minutes do you typically exercise in a week?” Responses from the women in the class were as follows:60, 240, 0, 360, 450, 200, 100, 70, 240, 0, 60, 360, 180, 300, 0, 270 Responses from the men in the class were as
Do students sleep more in Pennsylvania or in California?Data from surveys in elementary statistics classes at Penn State University and the University of California at Davis resulted in the following summary statistics for the number of hours students sleep:
Example 11.7 (p. 417) presented results for the number of hours slept the previous night from a survey given in two statistics classes. One class was a liberal arts class; the other class was a general introductory class. The survey was given following a Sunday night after classes had started. For
Example 11.3 (p. 410) presented data from a study in which sedentary men were randomly assigned to be placed on a diet or exercise for a year to lose weight. Forty-two men were placed on a diet, while the remaining 47 were put on an exercise routine. The group on a diet lost an average of 7.2 kg,
Case Study 1.1 presented data given in response to the question “What is the fastest you have ever driven a car (mph)?”The summary statistics are:Females: n 5 102, mean 5 88.4, standard deviation 5 14.4 Males: n 5 87, mean 5 107.4, standard deviation 5 17.4 Assuming that these students
Example 2.16 (p. 46) gave the weights of eight rowers on each of the Cambridge and Oxford crew teams. The weights are shown again here. Assume that these men represent appropriate random samples from the population of members of these crew teams over all time. Test the hypothesis that the mean
◆ Do hardcover and softcover books likely to be found on a professor’s shelf have the same average number of pages?
◆ The data in Example 13.1, on body temperature for young adults, was part of a larger set of body temperatures taken on 100 adults at a blood donor center. The data are in the file bodytemp on the website for this book. The Minitab output below shows the results of the “2-sample t” procedure
Calculate the value of the unpooled test statistic t in each of the following situations. In each case, assume the null hypothesis is H0: m1 2 m2 5 0.a. x1 5 35, s1 5 10, n1 5 100; x2 5 33, s2 5 9, n2 5 81.b. The difference in sample means is 48, s.e.1x1 2 x22 5 22.13.52. Using the following
For each of the following situations, identify whether the appropriate test is a paired t-test or a two-sample t-test:a. Sixty students were matched by initial pulse rate, with the two with the highest pulse forming a pair, and so on.Within each pair, one student was randomly chosen to drink a
For each of the following situations, identify whether the appropriate test is a paired t-test or a two-sample t-test:a. The weights of a sample of 15 marathon runners were taken before and after a training run to test whether marathon runners lose dangerous levels of fluids during a run.b. Random
In each of the following situations, determine whether the alternative hypothesis was Ha: m1 2 m2 . 0, Ha: m1 2 m2 , 0, or Ha: m1 2 m2 2 0.a. H0: m1 2 m2 5 0, t 5 2.33, df 5 8, p-value 5 .048.b. H0: m1 2 m2 5 0, t 5 22.33, df 5 8, p-value 5 .976.
In each of the following situations, determine whether the alternative hypothesis was Ha: m1 2 m2 . 0, Ha: m1 2 m2 , 0, or Ha: m1 2 m2 2 0.a. H0: m1 2 m2 5 0, t 5 22.33, df 5 8, p-value 5 .024.b. H0: m1 2 m2 5 0, t 5 2.33, df 5 8, p-value 5 .976.
This is Thought Question 13.2. Read Example 13.2 on page 508. Suppose that the purpose of the study was to determine whether pilots should be allowed to consume alcohol the evening prior to their flights, and that in this study the alcohol consumption occurred 12 hours before the measurement of the
Many people have high anxiety about visiting the dentist.Researchers want to know if this affects blood pressure in such a way that the mean blood pressure while waiting to see the dentist is higher than it is an hour after the visit. Ten individuals have their systolic blood pressures measured
A company manufactures a homeopathic drug that it claims can reduce the time it takes to overcome jet lag after longdistance flights. A researcher would like to test that claim.She recruits nine people who take frequent trips from San Francisco to London and assigns them to take a placebo for one
Although we have not emphasized it, the paired t-test can be used to test hypotheses in which the null value is something other than 0. For example, suppose that the proponents of a diet plan claim that the mean amount of weight lost in the first 3 weeks of following the plan is 10 pounds. A
In Case Study 3.1 (p. 97), results were presented for a sample of 63 men who were asked to report their actual weight and their ideal weight. The mean difference between actual and ideal weight was 2.48 pounds, and the standard deviation of the differences was 13.77 pounds. Is there sufficient
Refer to Exercise 13.38. Carry out all parts of the Exercise, but in parts (c) and (d) use the rejection region method, that is, use the Substitute Steps 3 and 4 described on pages 506–507 instead of finding the p-value.13.41. Refer to Exercise 13.39. Carry out the hypothesis test using the
Most people complain that they gain weight during the December holidays, and Yanovski et al. (2000) wanted to determine if that is the case. They sampled the weights of 195 adults in mid-November and again in early to mid-January.The mean weight change for the sample was a gain of 0.37 kg, with a
a study was reported in which students were asked to place as many dried beans into a cup as possible in 15 seconds with their dominant hand, and again with their nondominant hand (in randomized order). The differences in number of beans (dominant hand–nondominant hand) for 15 students were as
◆ In Exercise
◆ Data from the dataset UCDavisl on the companion website included information on height (height) and mother’s height (momheight) for 93 female students. Here is the output from the Minitab paired t procedure comparing these heights:
Give the value of the test statistic t in each of the following situations, and then find the p-value or p-value range for a two-tailed test.a. H0: md 5 0, d 5 4, sd 5 15, n 5 50.b. H0: md 5 0, d 5 0, sd 5 15, n 5 50.
Give the value of the test statistic t and the p-value or p-value range for this situation: H0: md 5 0, Ha: md ≠ 0, d 5 24, sd 5 15, n 5 50.
Suppose you were given a data set consisting of pairs of observations for which the question of interest was whether or not the population mean of the differences was 0.Explain the steps you would take to determine whether it is valid to use a paired t-test.
Explain how a paired t-test and a one-sample t-test are different and how they are the same.
This exercise is part of Thought Question 13.1. Consider a one-sample t-test with the one-sided alternative hypothesis Ha: m , m0.a. What range of values of the test statistic t would result in a p-value . .5?b. What range of values of the sample mean would result in a p-value . .5?c. Write a
Refer to Exercise 13.30. The following data are the heights for the 38 females who said they prefer to sit in the front of the classroom 66, 63, 63, 66, 65.5, 63, 60, 64, 63, 68, 68, 66, 62.5, 65, 64, 63, 66, 63, 63, 67, 66, 66, 62, 65, 63.5, 60, 61, 62, 63, 60, 65, 62, 63, 63, 62, 65, 63, 66 The
◆ The survey in the UCDavis2 dataset on the companion website asked students if they preferred to sit in the front, middle, or back of the class and also asked them their heights. The following data are the heights for 15 female students who said they prefer to sit in the back of the class.68,
A university is concerned that it is taking students too long to complete their requirements and graduate; the average time for all students is 4.7 years. The dean of the campus honors program claims that students who participated in that program in their first year have had a lower mean time to
Refer to Exercise 13.26. Carry out the hypothesis test using the rejection region method, that is, using the Substitute Steps 3 and 4 described on pages 506–507 instead of finding the p-value. Use a 5 .05.
Refer to Exercise 13.25. Carry out the hypothesis test in part(c) using the rejection region method, that is, using the Substitute Steps 3 and 4 described on pages 506–507 instead of finding the p-value. Use a 5 .05.
psi and 3 psi, respectively. Carry out the five steps to test the appropriate hypotheses using a 5 .05. (Use a p-value, not a rejection region.)

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