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

Refer to Exercise 12.44. In each of the parts, define in words the population parameter p.
In each of the following, determine whether the conditions for conducting a z-test for a proportion are met. If not, explain why not.a. A company employs 500 stockbrokers. They are all surveyed to find out whether a majority believes the market will go up in the next year.H0: p 5 .50 Ha: p . .50b.
In each of the following, determine whether the conditions for conducting a z-test for a proportion are met. If not, explain why not.a. Twenty students are randomly selected from the list of all sorority and fraternity members at a university to determine if a majority of sorority and fraternity
Refer to Exercise 12.41. For each of parts (a) to (d), specify the rejection region for a 5 .05, and then reach a conclusion for the test using the rejection region rule.
Find the p-value for each of these situations, taking into account whether the test is one-sided or two-sided.a. z-statistic 5 2.10, H0: p 5 .10, Ha: p ≠ .10.b. z-statistic 5 2.00, H0: p 5 .6, Ha: p , .6.c. z-statistic 5 21.09, H0: p 5 .5, Ha: p , .5.d. z-statistic 5 4.25, H0: p 5 .25, Ha: p .
A researcher is deciding whether to use a level of significance equal to .05 or a level of significance equal to.01. Explain how this choice will affect the power of the hypothesis test.
A researcher is deciding whether to use a sample size of 100 or whether to increase the sample size to 200. Explain how this choice will affect the power of any hypothesis tests conducted using data from the resulting sample.
Refer to Exercise 12.24, in which a woman thinks that she might be pregnant so she takes a pregnancy test. This situation is analogous to hypothesis testing.a. Explain in words what a Type 1 error would be in this situation.b. Explain in words what a Type 2 error would be in this situation.c. Which
A politician is trying to decide whether to vote for a new tax bill that calls for substantial reforms. A random sample of voters in his district leads him to believe the alternative hypothesis, Ha: p . .5, where p is the proportion of all voters in his district who support the bill. As a
Explain which type of error, Type 1 or Type 2, could be made in each of the following cases.a. The null hypothesis is true.b. The alternative hypothesis is true.c. The null hypothesis is not rejected.d. The null hypothesis is rejected.
Consider medical tests, in which the null hypothesis is that the patient does not have the disease and the alternative hypothesis is that the patient has the disease.a. Give an example of a medical situation in which a Type 1 error would be more serious.b. Give an example of a medical situation in
Medical researchers now believe there may be a link between baldness and heart attacks in men.a. State the null hypothesis and the alternative hypothesis for a study used to investigate whether or not there is such a relationship.b. Discuss what would constitute a Type 1 error in this study.c.
A medical insurance company wants to know whether the proportion of its customers requiring a hospital stay during a year will decrease if it provides coverage for certain types of alternative medicine. The company conducts a 1-year study in which it gives insurance coverage for alternative
This is also Exercise 1.20. Explain what is meant by a “false positive” in the context of conclusions in statistical studies.
Define events as follows: A 5 Null hypothesis is true.AC 5 Alternative hypothesis is true. B 5 Null hypothesis is not rejected. BC 5 Null hypothesis is rejected. For each of the following outcomes, explain whether a Type 1 error, a Type 2 error, or a correct decision has been made.a. A and B.b. AC
Can the two types of error both be made in the same hypothesis test? Explain.
Explain whether each of the following statements is true or false.a. The p-value is the probability that the null hypothesis is true.b. If the null hypothesis is true, then the level of significance is the probability of making a Type 1 error.c. A Type 2 error can only occur when the null
A physician claims that as soon as his patients have a positive pregnancy test, he is generally able to predict the sex of the baby and that his probability of being right is greater than the one-half that would be expected if he were just guessing. A skeptic challenges his claim, and the physician
Two researchers are testing the null hypothesis that a population proportion p is .25 and the alternative hypothesis that p . .25. Both take a sample of 100 observations. Researcher A finds a sample proportion of .29, and Researcher B finds a sample proportion of .33. For which researcher will the
An article in USA Today (Elias, June 3, 1999, p. D1) describes a study done by Georgia State University psychologist James Dabbs in which he found that women who are trial lawyers(litigators) are more likely to have male children than are women lawyers who are not trial lawyers. According to the
About 10% of the human population is left-handed. Suppose that a researcher speculates that artists are more likely to be left-handed than are other people in the general population.
Suppose that a woman thinks she might be pregnant, so she takes a pregnancy test. Considering this situation to be analogous to hypothesis testing, write each of the following in words.a. The null hypothesis. (Hint: Remember that the null hypothesis generally states that there is nothing going
Suppose that the value of a test statistic falls into the rejection region for the test. Will the p-value be less than the specified level of significance? Explain.
Given the convention of declaring that a result is “statistically significant” if the p-value is .05 or less, what decision would be made concerning the null and alternative hypotheses in each of the following cases? Be explicit about the wording of the decision.a. p-value 5 .35.b. p-value 5
Consider testing the null hypothesis that there is no relationship between smoking and getting a certain disease versus the alternative hypothesis that smokers are more likely than nonsmokers to get the disease. Explain in words what would be concluded about the relationship in the population ifa.
Consider this quote: “In a recent survey, 61 out of 100 consumers reported that they preferred plastic bags instead of paper bags for their groceries. If there is no difference in preference in the population, the chance of such extreme results in a sample of this size is about .03. Because .03
State the conclusion that would be made in each of the following situations.a. Level of significance 5 .05, p-value 5 .10.b. Level of significance 5 .05, p-value 5 .01.c. Level of significance 5 .01, p-value 5 .99.d. Level of significance 5 .01, p-value 5 .002.
Suppose that the sticker on a new car states that the car gets 32 miles per gallon for highway driving. Marisa wants to test that hypothesis.a. Write the null hypothesis in symbols. Remember from Chapter 9 that the symbol for one population mean is m.b. What is the null value in this situation?
Suppose that a null hypothesis, in words, is that the mean weight for the population of newborn babies is the same in the United States as it is in England.a. Write the null hypothesis in symbols. Use Example 12.3 on p. 453 for guidance.b. What is the null value in this situation?
Refer to Exercise 12.14. In each of the two situations, the hypotheses are about a population proportion p. Explain what the population is and what the proportion of interest is in each case.
In the last census, it was determined that 6% of school-aged children in a certain state lived with their grandparent(s).Suppose that to support a bill on tax breaks for seniors, a congressional member plans to take a random sample of school-aged children to determine if that percentage has
For each of the following situations, write the null and alternative hypotheses in words and in symbols (as in Example 12.2, p. 453).a. An anthropologist is trying to determine if the people in a certain region are descended from the same ancestors as those in another region she has studied. She
Do you think researchers should determine whether to use a one-sided or two-sided hypothesis test before they look at the sample data or after they look at it? Explain.
Answer Thought Question 12.1 on page 455.
Suppose that a statistics teacher asks his students to each randomly pick one of the numbers 0, 1, 2, 3, 4. His general
Suppose that the present success rate in the treatment of a particular psychiatric disorder is .65 (65%). A research group hopes to demonstrate that the success rate of a new treatment will be better than this standard. Use the letter p to represent the success rate of the new treatment. Write null
State the null and alternative hypotheses for each of the following potential research questions. In each situation, also indicate whether the hypothesis test will be one-sided or two-sided.a. Will an increase in the speed limits on interstate highways lead to an increase in the highway fatality
State the null and alternative hypotheses for each of the following potential research questions. In each situation, also indicate whether the hypothesis test will be one-sided or two-sided.a. Do female college students study more, on average, than male college students do?b. Compared to men who
In each part, is the statement a valid null hypothesis? If not, explain why not.a. In a sample of students, the mean pulse rate for the men is equal to the mean pulse rate for the women.b. The average weight of newborn boys is the same as the average weight of newborn girls.c. The proportion of
For each of the following situations, write the alternative hypothesis.a. The null hypothesis is H0: p 5 .30, and it is a two-sided hypothesis test.b. The null hypothesis is H0: p # .45.c. The null hypothesis is H0: p $ .60.
Determine whether each of these statements is an example of a null hypothesis or an example of an alternative hypothesis.a. The average weight of Canadian geese is the same as the average weight of Canadian warblers.b. The proportion of books in the local public library that are novels is higher
Retired professional tennis players Martina Navratilova, Monica Seles, John McEnroe, and Jimmy Connors are all left-handed. Define the parameter p to be the proportion of professional tennis players (current and retired) who are left-handed. Researchers are interested in the hypothesis that p .
Define the parameter p1 2 p2 to be the difference in the proportions of 21-year-old men and women in the United States who have a high school diploma. Researchers are interested in the hypothesis that p1 2 p2 5 0.a. What are the populations of interest in this situation?b. Write the hypothesis in
One example of a possible hypothesis of interest given on p. 452 is whether or not the proportion favoring the death penalty is the same for teenagers as it is for adults.a. What are the populations of interest in this situation?b. Specify the population parameter of interest.c. Write the
One example of a possible hypothesis of interest given on pp. 451–452 is based on the fact that full moons occur on average every 29.53 days, and we might classify babies as to whether or not they were born during the 24-hour period surrounding a full moon. The hypothesis of interest is that the
For this exercise, use the deprived dataset on the companion website. Students in a statistics class were asked whether they generally felt sleep deprived (variable name 5 Deprived) and also were asked how many hours they usually slept per night (variable name 5 SleepHrs).a. For the sample, find
For this exercise, use the cholest dataset on the companion website. The variable control contains cholesterol levels for individuals who have not had a heart attack, while the variable 2-day contains cholesterol levels for heart attack patients 2 days after the attack.a. Calculate a 98% confidence
For this exercise, use the dataset UCDavis2 on the companion website. In the survey, students reported ideal height(IdealHt) and actual height (height).
For this exercise, use the dataset pennstate1 on the companion website. The variable RtSpan has the raw data for measurements of the stretched right handspans of n 5 190 Penn State students.a. Calculate a 95% confidence interval for the mean stretched handspan in the population of men represented
For this exercise, use the dataset pennstate1 on the companion website. Case Study 1.1 presented data given by college students in response to the question, “What is the fastest you have ever driven a car? mph” The variable fastest contains the responses to this question. Determine a 95%
Suppose that 100 researchers each plan to independently gather data and construct a 90% confidence interval for a population mean. If X 5 the number of those intervals that actually cover the population means, then X is a binomial random variable.a. What is a “success” for this binomial random
In Example 11.11 (p. 427), we compared the time in seconds to cross an intersection when someone was or was not staring at the driver. We did not assume equal population variances. Following is the Minitab (Version 16) output that resulted from clicking “Assume Equal Variance.”
Examples 11.2, 11.6, and 11.8 in Sections 11.1 and 11.2 used a sample of n 5 175 students to estimate the mean daily hours that Penn State students watch television. The following summary shows results for daily hours of television by sex:
A study was conducted on pregnant women and the subsequent development of their children (Olds et al., 1994). One of the questions of interest was whether the IQ of children would differ for mothers who smoked at least 10 cigarettes a day during pregnancy and those who did not smoke at all.The mean
In a random sample of 199 married British couples (described in Chapter 2), there were 170 for which both ages were reported. The average difference in husband’s age and wife’s age was 2.24 years, with standard deviation of 4.1 years.a. Find an approximate 95% confidence interval for the
◆ An experiment was performed by 15 students in a statistics class at the University of California-Davis to determine whether manual dexterity was better for the dominant hand compared to the nondominant hand (left or right). Each student measured the number of beans they could place into a cup
This is also Thought Question 11.3. Refer to Example 11.8, in which a confidence interval was found for the mean number of hours that Penn State students watch TV.
In Stroop’s Word Color Test, 100 words that are color names are shown in colors different from the word. For example, the word red might be displayed in blue. The task is to correctly identify the display color of each word; in the example just given the correct response would be blue.Gustafson
Example 2.16 (p. 46) gave the weights in pounds of the 18 men on the crew teams at Oxford and Cambridge universities in 1991–1992. The data were as follows:Cambridge: 188.5, 183.0, 194.5, 185.0, 214.0, 203.5, 186.0, 178.5, 109.0 Oxford: 186.0, 184.5, 204.0, 184.5, 195.5, 202.5, 174.0, 183.0,
Refer to Exercise 11.75. The sample included the heights of the women’s husbands as well. For these men, the mean height was 1732.5 mm with standard deviation 68.8 mm.a. Find a 90% confidence interval for the mean height of the population of men represented by this sample.b. Given the information
Example 2.17 (p. 47) reported that a random sample of 199 married British women had a mean height of 1602 mm with standard deviation of 62.4 mm.a. Find a 99% confidence interval for the mean height of all women represented by this sample. Write a sentence interpreting the interval.b. Give a 99%
Find an exact 95% confidence interval (use t*) for the mean weight loss after a year of exercise for the population of men represented by those in the study in Example 11.3 (p. 410).There were 47 men in the exercise group in the sample, with mean weight loss of 4.0 kg and standard deviation of 3.9
In computing a confidence interval for a population mean m, explain whether the interval would be wider, more narrow, or neither as a result of each of the following changes. Assume that features that are not mentioned (confidence level, mean, standard deviation, sample size) remain the same.a. The
Write a definition of the confidence level for a confidence interval procedure.
For the same random sample, give the 90%, 95%, and 99%confidence intervals for the population mean. (This can be done by observing what occurs when the scrollbar is used to change the confidence level.) What is indicated about the relationship between the width of the confidence interval and the
using the 99% confidence level.
Change the confidence level to 99%. Repeat the parts of Exercise
Change the confidence level to 95%. Repeat the parts of Exercise 11.68 using the 95% confidence level.
Set the confidence level at 68%.a. Use the sample! button to generate a new random sample. Write the confidence interval displayed, and indicate whether or not it captures the population mean (170).
Refer to Case Study 11.2 (pp. 435–436).a. Use the baseline data to find an approximate 95% confidence interval for the difference in means for the populations represented by the placebo and calcium groups at the start of the study.b. Explain why the researchers would want the interval computed in
Refer to Case Study 11.2 (pp. 435–436). Use the baseline data for the placebo group to find an approximate 95% confidence interval for the mean PMS complex score for the population of all women like the ones in this study. Write a sentence interpreting the interval.
In a 12-year study done at ten medical centers, Cole et al.(2000) investigated whether the decrease in heart rate over the first 2 minutes after stopping treadmill exercise was a useful predictor of subsequent death during the study period. Based on observations of n 5 5234 participants, the
Suppose that you were given a 95% confidence interval for the relative risk of disease under two different conditions.What could you conclude about the risk of disease under the two conditions if:a. The confidence interval did not cover 1.0?b. The confidence interval did cover 1.0?
Refer to Exercise 11.62. Sample statistics summarizing the data on number of CDs are x 5 72.84, s 5 72, n 5 205. Use this information to verify the 95% confidence interval for the mean of 62.9 to 82.8 given in part (b).
◆ Responses from n 5 204 college students to the question,“About how many CDs do you own?” are used to determine 95% confidence intervals for the median and the mean. (Data source: pennstate2 dataset on the companion website)
Refer to Exercises 11.32 and 11.54. Use the pooled procedure to compute a 95% confidence interval for the difference in mean days of symptoms for the zinc and placebo treatments. (Use placebo 2 zinc.)
Following are data for 20 individuals on resting pulse rate and whether or not the individual regularly exercises.
What assumption is necessary in order to use the pooled procedure for finding a confidence interval for the difference between two population means?
Refer to the output for Exercise 11.52 about letters printed with the nondominant hand.a. Find the value of sp 5 pooled standard deviation for these data.b. For the pooled two-sample procedure, find the (pooled)standard error of the difference in sample means.c. What would be the degrees of freedom
Refer to Exercises 11.17 and 11.18, in which the foot lengths of a random sample of 64 men had a mean of 27.5 cm and a standard deviation of 2 cm, while a random sample of 100 women had a mean foot length of 24.0 cm and a standard deviation of 2 cm. Compute an approximate 95%confidence interval for
In Example 11.12 (p. 428), we learned about a study of hangover symptoms in college students (Slutske et al., 2003, on the website for this book). The students answered questions about alcohol use and hangovers, including a count of how many out of a list of 13 possible hangover symptoms that they
cm with a standard deviation equal to 1.8 cm.a. Find the value of the difference between the sample means for men and women. (Use men 2 women.)b. Find the standard error of the difference between the sample means in this context.c. Find an approximate 95% confidence interval for the difference
For a sample of 36 men, the mean head circumference is 57.5 cm with a standard deviation equal to 2.4 cm. For a sample of 36 women, the mean head circumference is
Refer to Exercise 11.32 about the effect of zinc lozenges on the duration of cold symptoms. For n 5 25 in the zinc lozenge group, the mean overall duration of symptoms was 4.5 days, and the standard deviation was 1.6 days. For n 5 23 in the placebo group, the mean overall duration of symptoms was
Data on the testosterone levels (ng/dL in saliva) of men in different professions were given in a paper published in the Journal of Personality and Social Psychology (Dabbs et al., 1990). The researchers suggest that there are occupational differences in mean testosterone level. Medical doctors and
◆ Each of 63 students in a statistics class used her or his nondominant hand to print as many letters of the alphabet, in order, as they could in 15 seconds. The following output for this exercise gives results for a 95% confidence interval for the difference in population means for females and
Suppose that you were given a 95% confidence interval for the difference in two population means. What could you conclude about the population means ifa. The confidence interval did not cover zero?b. The confidence interval did cover zero?
For a sample of n 5 20 women aged 18 to 29, responses to the question “How tall would you like to be?” are recorded along with actual heights. In the sample, the mean desired height is 66.7 inches, the mean actual height is 64.9 inches, and the mean difference is d 5 1.8 inches. The standard
Refer to Exercise 11.48.a. Find a 95% confidence interval for the mean difference in weights for the first and second baby for the population of women who have had at least two children.b. Would it be appropriate to use the method given on page 420 for finding an approximate 95% confidence interval
A researcher was interested in knowing whether the mean weight of the second baby is higher, lower, or about the same as the mean weight of the first baby for women who have at least two children. She selected a representative sample of 40 women who had at least two children and asked them for the
If a confidence interval for md covers 0, can we conclude that the population means for the two measurements are identical? Explain.
A random sample of five college women was asked for their own heights and their mothers’ heights. The researchers wanted to know whether college women are taller on average than their mothers. The results (in inches) follow:a. Define the parameter of interest in this situation.b. Find a 95%
In Example 11.9 (p. 422), we compared the number of hours of computer time with the number of hours watching TV by finding a 90% confidence interval.a. Find a 95% confidence interval for this situation, and write a sentence interpreting it.b. On the basis of the 95% confidence interval, can we
In Example 11.10 (p. 424), we found a 95% confidence interval for the mean reduction in trait anxiety if everyone in the population were to take the meditation training offered in the study. For the 21 people in the study, the mean reduction in anxiety was 4.5, and the standard deviation was 7.2.a.
Explain why the approximation for a 95% confidence interval for a mean that uses the value 2 as multip
Example 11.3 (p. 410) described a study that compared mean weight loss for a diet plan to mean weight loss for an exercise plan. In the study, n 5 42 men were put on a diet.The men who dieted lost an average of 7.2 kg, with a standard deviation of 3.7 kg.a. Compute the standard error of the mean
This scenario was presented in Exercise 11.17, which asked for the standard error of the mean: Suppose that a randomly selected sample of 64 men has a mean foot length of 27.5 cm, and the standard deviation of the sample is 2 cm.Calculate an approximate 95% confidence interval for the mean foot
(b) and (c), which asked for the standard error of the mean. Find the standard error of the mean, and then find an approximate 95% confidence interval for the population mean, using the approximation that is appropriate for large samples.a. Mean systolic blood pressure for a sample of n 5 100 men
The following two scenarios were presented in Exercise
The following scenario was presented in Exercise 11.16a, which asked for the standard error of the mean. Find the standard error of the mean, and then find an approximate 95% confidence interval for the population mean, using the approximation that is appropriate for large samples.Scenario: The

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