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Mind On Statistics 4th Edition David D Busch, Jessica M Utts, Robert F Heckard - Solutions
Compare the formula for an approximate 95% confidence interval given on page 420 in Lesson 2 with the general formula for a confidence interval in the formula box on page 420 in Chapter 10.a. What is different about the two formulas?b. In finding a confidence interval for one population mean, what
In Example 11.6 (p. 415), we found that a 99% confidence interval for the mean number of hours Penn State students watch television in a day is 1.76 to 2.42 hours. Explain whether each of the following statements is a correct interpretation of this result.a. We can be fairly confident that 99% of
Suppose that a highway safety researcher is studying the design of a highway sign and is interested in the mean maximum distance at which drivers are able to read the sign. The maximum distances (in feet) at which n 5 16 drivers can read the sign are as follows:
Refer to Exercise 11.34. Use the Empirical Rule to create an interval that estimates the textbook expenses of 95% of the individual students at the university (not the mean).
A randomly selected sample of n 5 12 students at a university is asked, “How much did you spend for textbooks this semester?” The responses, in dollars, are 200, 175, 450, 300, 350, 250, 150, 200, 320, 370, 404, 250
Refer to Exercise 11.32. Compute a 99% confidence interval for the mean duration of symptoms for individuals using the placebo lozenges. Write one or two sentences that interpret this interval.
Volunteers who had developed a cold within the previous 24 hours were randomized to take either zinc or placebo lozenges every 2 to 3 hours until their cold symptoms were gone (Prasad et al., 2000). Twenty-five participants took zinc lozenges, and 23 participants took placebo lozenges. The mean
What three factors affect the width of a confidence interval for a population mean? For each factor, indicate how an increase in the numerical value of the factor affects the interval width.
The age at first marriage is found for a random sample of n 5 81 women who graduated from college in 1980. The mean age is x 5 25.5, and the standard deviation is s 5 4.5 years.a. Find the value of the standard error of the sample mean.Write a sentence that interprets this value. (Refer to Section
A random sample of n 5 9 men between 30 and 39 years old is asked to do as many sit-ups as they can in one minute. The mean number is x 5 26.2, and the standard deviation is s 5 6.a. Find the value of the standard error of the sample mean.Write a sentence that interprets this value. (Refer to
Use Table A.2 to find the multiplier t* for calculating a confidence interval for a single population mean in each of the following situations.a. n 5 25; confidence level 5 .95.b. n 5 81; confidence level 5 .95.c. n 5 1001, confidence level 5 .99
Use Table A.2 to find the multiplier t* for calculating a confidence interval for a single population mean in each of the following situations.a. n 5 22; confidence level 5 .98.b. n 5 5; confidence level 5 .90.c. n 5 5; confidence level 5 .99.
In each case, use the information given to compute a confidence interval for the population mean m. Assume that all necessary conditions are present for using the method described in Section 11.2.a. x 5 76, s 5 8, n 5 16, 95% confidence level.b. x 5 100, s 5 8, n 5 16, 95% confidence level.c. x 5
In each case, use the information given to compute a confidence interval for the population mean m. Assume that all necessary conditions are present for using the method described in Section 11.2.a. x 5 76, s 5 6, n 5 9, 95% confidence level.b. x 5 76, s 5 6, n 5 9, 90% confidence level.c. x 5 76,
Refer to Figure 11.3 (p. 412), in which the relationship between t* and the 95% confidence level is illustrated for df 5 24. Draw a similar picture for df 5 24 and 90%confidence.
Explain what happens to the value of t* in each of the following cases.a. The confidence level is increased from 90% to 95%.b. The sample size is increased.c. The degrees of freedom are increased.d. The degrees of freedom are essentially infinite.e. The standard error of the mean is decreased
Suppose that a teacher asks her class how many hours they studied for the midterm exam. For the 40 students who are enrolled in the class, the mean was 5.5 hours, and the standard deviation was 2 hours. Explain why the teacher should not calculate a standard error for the mean, and why she should
Note that the standard error formulas for means all involve sample standard deviations and sample sizes. With this knowledge, what can a researcher do, when designing a study, to try to make sure the standard error isn’t so large that it produces a meaningless confidence interval?
If each of the following is decreased but everything else remains the same, will a confidence interval become wider, will it become narrower, or will the width remain the same?Explain.a. The sample estimate.b. The standard error.c. The confidence level.
The pulse rates of n 5 50 people are measured. These people then march in place for 1 minute, and the pulse rates are measured again. We are interested in estimating the mean difference between the two pulse rates for the population represented by this sample. Explain how you would compute the
Refer to Exercise 11.17 about the foot lengths of men. A randomly selected sample of n 5 100 women has a mean foot length of x 5 24.0 cm, and the standard deviation of the sample is 2 cm.a. Calculate the standard error of the mean. Explain why the value is smaller than the standard error for the
Suppose that a randomly selected sample of n 5 64 men has a mean foot length of x 5 27.5 cm, and the standard deviation of the sample is 2 cm. Calculate the standard error of the sample mean. Write one or two sentences that interpret this value.
In the description of independent samples on page 408, four common methods were given for generating independent samples. They are repeated in the parts of this exercise. In each case, give an example of a research question for which independent samples would be collected using the method described.
In the definition of paired data on page 407, three ways in which paired data can occur were given. They are repeated in the parts of this exercise. In each case, given an example of a research question for which paired data would be collected using the method described.a. The same measurement is
For each of the following research questions, would it make more sense to collect paired data or independent samples?Explain.a. What is the mean difference in height for the male and female in fraternal twin pairs in which there is one of each sex?b. What is the difference in mean heights for males
For each of the following research questions, would it make more sense to collect paired data or independent samples?Explain.a. What is the difference in the mean price of gasoline for all gas stations in the United States last week and this week?b. How does the mean weight of adults in college
Researchers at the MIND Institute at the University of California-Davis analyzed the blood of 70 autistic and 35 nonautistic children between the ages of 4 and 6 (Lau, 2005).One marker that they examined was B cells, which is a type of immune cell that produces antibodies in the blood. They found
Give an example of a research question (not covered in this chapter) for which the appropriate parameter isa. m.b. md.c. m1 2 m2.
A multinational company plans to open new offices in one of two countries where it has not operated before and is trying to decide which country to choose. One feature that the company is interested in is how much vacation time it will need to offer employees in the two countries to be competitive
Use software, a calculator, or Table A.2 to find the value of t*for each of the following situations.a. df 5 18, 99% confidence level.b. df 5 100, 95% confidence level.c. n 5 41, 90% confidence interval for one mean.
Use software, a calculator or Table A.2 to find the value of t*for each of the following situations.a. df 5 15, 95% confidence level.b. df 5 30, 90% confidence level.c. n 5 10, 95% confidence interval for one mean.
In each part, use the information to calculate the appropriate standard error of the mean.a. The mean height for a sample of n 5 25 children is x 5 36 inches, and the standard deviation is s 5 1.0 inch.b. A sample of n 5 100 women went on a diet and lost an average of d 5 9 pounds. The standard
In each part, use the information given to calculate the appropriate standard error.a. One mean, n 5 100 and standard deviation s 5 15.b. Mean for paired differences, n 5 49 and standard deviation of the differences sd 5 21.c. Difference in means for independent samples, n1 5 n2 5 50 and s1 5 s2 5
You have been told that for university classes, students are supposed to spend 2 hours working outside of class for each hour in class. You are curious to know the average amount of time that students at your school spend working outside of class. You contact what you think is a representative
In each part, identify whether it would be more appropriate to use a procedure for paired data or a procedure for two independent samples to estimate the difference of interest.a. A researcher wants to estimate the difference between the mean scores on a memorization test for people over 60 years
Would it be appropriate to use the ages of death of First Ladies given in Chapter 2 (Table 2.5, p. 28) to find a 95%confidence interval for the mean? If your answer is yes, what is the parameter of interest? If your answer is no, explain why not.
Suppose that you are told that the mean IQ score for children in a particular school is 105.3. Explain what additional information you would need in order to know whether the mean of 105.3 is a statistic or a parameter.
Use the dataset GSS-08 on the companion website. The variable owngun indicates whether or not the respondent owns a gun, and the variable polparty contains the respondent’s political party pref erence.a. Determine a 95% confidence interval for the difference in the proportions of Republicans and
Refer to Exercise 10.91 about the variable atfirst in the pennstate3 dataset on the companion website.a. Create a two-way table that shows the relationship between the variables atfirst and Sex. (See Sections 2.3 and 4.1 to review two-way tables.)b. What proportion of the females in the sample
For this exercise, use the pennstate3 dataset on the companion website. The data are from a student survey in a statistics class at Penn State. The variable atfirst gives data for whether or not a student believes in love at first sight.
For this exercise, use the GSS-08 dataset on the companion website. The dataset contains data from the 2008 General Social Survey, and the variable marijuan indicates the respondent’s opinion about the legalization of marijuana.a. Calculate a 95% confidence interval for the proportion of
on page 380. 10.89 For this exercise, use the GSS-08 dataset on the companion website. The dataset contains data from the 2008 General Social Survey, and the variable polparty indicates the political party preference of the respondent.a. Calculate a 95% confidence interval for the proportion of
Answer Thought Question
Fatty acids that are present in fish oil may be useful for treating some psychiatric disorders. An article reported on September 3, 1998, at the Yahoo Health website described a randomized experiment done by a Harvard Medical School researcher in which 14 bipolar patients received fish oil daily,
For each of the following, explain whether it affects the width of a confidence interval, the center of a confidence interval, neither, or both.a. The sample estimate, for the situations involving means.b. The multiplier.c. The standard error of the estimate.d. The confidence level.e. The sample
In the table below are data collected between 1996 and 1998 on ear piercing and tattoos for male Penn State students.Assume that these men represent a random sample of male Penn State students. The results were as follows
◆ A sample of college students was asked whether they would return the money if they found a wallet on the street.Of the 93 women, 84 said “yes,” and of the 75 men, 53 said“yes.” Assume that these students represent all college stu dents (Data source: UCDavis2 dataset on the companion
Refer to Exercise 10.81. Calculate a 95% confidence interval for the proportion of American men who would say that they have ever driven a car when they probably have had too much to drink, and write a sentence or two that interprets the interval. Be specific about the population that the interval
Find the reported results of a poll in which a margin of error is also reported. Look on the Internet, in a weekly news magazine such as Newsweek or Time, or a newspaper such as the New York Times or USA Today.a. Explain what question was asked in the poll and what margin of error was reported.
On January 30, 1995, Time magazine reported the results of a poll of adult Americans in which it asked, “Have you ever driven a car when you probably had too much alcohol to drive safely?” The exact results were not given, but from the information given, we can guess at what they were. Of the
Refer to Exercise 10.79, which reported results for the numbers of men and women who had a tattoo.a. Find a 90% confidence interval for the difference in population proportions of men and women with a tattoo.b. On the basis of the interval that you computed in part (a), formulate a conclusion about
In 1998, two statistics classes for students in the liberal arts at a large northeastern university were asked, “Do you have a tattoo?” The responses were as follows:a. What proportion of the women in this sample has a tattoo?b. What proportion of the men in this sample has a tattoo?c. Compare
Refer to Exercise 10.77, in which two different wordings of a question were used to estimate the proportion of Americans who are in favor of the death penalty.a. Verify that the conditions are met to compute a confidence interval for the difference in two population proportions, where they are the
The Gallup Organization used two different wordings of a question in a February 1999 poll about the death penalty.The two different questions were asked of two different random samples of Americans. Results reported at the Gallup website follow.Question 1: Are you in favor of the death penalty for
Refer to the derivation of a 95% confidence interval for p on page 381 in Lesson 2 of Section 10.2. Use a similar argument to explain why a 68% confidence interval for p is “Sample estimate 6 Standard error.”
A professor wants to know whether her class of 60 students would prefer the final exam to be given as a take-home exam or an in-class exam. She surveys the class and learns that 45 of the 60 students would prefer a take-home. Explain why she should not use these data to compute a 95% confidence
Use an example from this chapter to explain the difference between a sample proportion and a population proportion.
Refer to Exercise 10.72. Find a 95% confidence interval for the difference in population proportions of male policemen and men of other occupations who have heart disease. On the basis of this confidence interval, is it safe to conclude that male police officers are more likely to experience heart
A study reported in the Journal of Occupational and Environmental Medicine (Franke et al., 1998, 40: 441–444)found that retired male Iowa policemen are more likely to have heart disease compared to other men with similar ages but different occupations. Data from the study were that about 32% of a
In Chapter 2, we saw data from a statistics class activity in which 190 students were asked to randomly pick one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The number 7 was picked by 56 students.a. For the sample, calculate the proportion of students who picked 7.b. Calculate the standard error
A federal law that lowered the limit for a legal blood alcohol level for automobile drivers was signed by President Clinton in October 2000. At its website, the Gallup Organization reported the following survey results in an article dated October 26, 2000:
In each situation, explain why you think that the sample proportion should or should not be used to estimate the population proportion.a. An Internet news organization asks visitors to its website to respond to the question, “Are you satisfied with the president’s job performance?” Of n 5
This exercise is also Exercise 1.32. A random sample of 1001 University of California faculty members taken in December 1995 was asked, “Do you favor or oppose using race, religion, sex, color, ethnicity, or national origin as a criterion for admission to the University of California?” (Roper
A survey is done to estimate the proportion of a population that favors a new tax law proposal for a city. In a randomly selected sample of n 5 400 city residents, 43% favor the proposal.a. Calculate a 95% confidence interval that estimates the population proportion in favor of the proposed law.b.
Suppose that a 95% confidence interval for the proportion of men who experience sleep apnea (irregular breathing during sleep) is .11 to .17 and a 95% confidence interval for the proportion of women who experience sleep apnea is.04 to .08.a. On the basis of these intervals, is it reasonable to
As was described in Exercise 10.61, a July 2002 Gallup poll of n 5 1004 randomly selected U.S. adults found that 55% felt that their weight was about right. In a similar poll in 1990, about 46% felt that their weight was about right. The margin of error for each poll was 3%.a. Based on these
Suppose that a 95% confidence interval for p1 2 p2 5 difference in proportions of college men and women who have ever missed a class due to drinking alcohol is .07 to.13. On the basis of this confidence interval can we infer that the population proportions ever having missed a class due to drinking
Suppose that a health expert has claimed that 16% of college students smoke cigarettes. To investigate this claim, researchers survey a random sample of college students.Using this sample, a 95% confidence interval for the percentage of college students who smoke is found to be 9% to 14%. On the
A university is contemplating switching from the quarter system to a semester system. The administration conducts a survey of a random sample of 400 students and finds that 240 of them prefer to remain on the quarter system.a. Construct a 95% confidence interval for the true proportion of all
A Gallup Organization poll of n 5 1004 randomly selected American adults in July 2002 found that 55% of those surveyed felt that their weight was about right. The margin of error for the survey was given as 3% (Source: http://www.gallup.com).a. Find a 95% confidence interval estimate of the
Refer to Exercise 10.52.a. Compute a 99% confidence interval for the difference in proportions.b. How does the width of the 99% confidence interval computed in part (a) of this problem compare to the width of the 95% confidence interval given in part (a) of Exercise 10.52?c. Would a 90% confidence
In a survey of college students, 70% (.70) of the 100 women surveyed said that they believe in love at first sight, whereas only 40% (.40) of the 80 men surveyed said that they believe in love at first sight.a. Find the value of the difference between the sample proportions for men and women.b.
In a CBS News survey done in 2009, 95% of n 5 346 randomly sampled married men said that they would marry their spouses again if they had it to do all over again. In the same survey, 85% of n 5 522 married women said that they would marry their spouses if they had it to do all over again (Source:
Refer to Exercise 10.55. In the sample, there were 4594 individuals with at least a college degree and n 5 7076 individuals with at least a high school diploma (but not a college degree). Following is Minitab output with a 95% confidence interval for the difference in proportions experiencing
Refer to the output given for Exercise 10.50.a. Find the value of s.e.1p^ 1 2 p^ 22 5 standard error of the difference between the two sample proportions.b. Find a 90% confidence interval for the difference between the population proportions opposed to the death penalty in the years 2008 and 1993.
In a study done in Maryland, investigators surveyed individuals by telephone about how often they get tension headaches (Schwartz et al., 1998). One response variable that was measured was whether or not the respondent had experienced an episodic tension-type headache (ETTH) in the prior year. A
A study was done to determine whether there is a relationship between snoring and the risk of heart disease (Norton and Dunn, 1985). Among 1105 snorers in the study, 85 had heart disease, while only 24 of 1379 nonsnorers had heart disease.a. Determine a 95% confidence interval that estimates p1 2
Suppose that a randomly selected sample of n 5 900 registered voters is surveyed to estimate the proportions that will vote for the two candidates in an upcoming election. Fiftyfive percent of those sampled say that they will vote for one candidate, while 45% indicate a preference for the other
◆ In Case Study 10.3 (p. 392), students in a statistics class at Penn State were asked, “Would you date someone with a great personality even though you did not find them attractive?” The results were that 61.1% of 131 women answered“yes,” while 42.6% of 61 men answered “yes” (Data
In each situation, explain whether the method covered in Section 10.3 for finding a confidence interval for the difference in two proportions should be used.a. A survey is done to estimate the difference between the proportions of college students and high school students who smoke cigarettes. Data
◆ In the General Social Survey, an ongoing nationwide survey done by the National Opinion Research Center at the University of Chicago, a question asked is whether a respondent favors or opposes capital punishment (the death penalty) for persons convicted of murder. The output for this exercise
In a survey reported in a special edition of Newsweek(Spring/Summer 1999, Health for Life), only 3% of a sample of 757 American women responded “Not at all satisfied” to the question, “How satisfied are you with your overall physical appearance?”a. The margin of error for the poll was
In a Gallup Youth Survey done in 2000, n 5 501 randomly selected American teenagers were asked about how well they get along with their parents.a. According to the Gallup Organization, the margin of error for the poll was 5%. Show how you think they determined this figure.
In Example 10.8 (p. 385), the information given was that 3% of a nationwide randomly selected sample of n 5 883 suffered from severe allergies.a. Determine the standard error of the sample proportion in this problem.b. Verify that the margin of error is about 1.1% for a 95%confidence interval for
Suppose that a polling organization is conducting a survey to estimate the proportion of Americans who regularly attend religious services. The organization plans to gather data from a randomly selected sample of 550 individuals.On the basis of the “conservative” estimate, what will be the
For each combination of sample size and sample proportion, find the margin of error for the 95% confidence level.Use the formula given on page 383.a. n 5 100, p^ 5 .56.b. n 5 400, p^ 5 .56.
For each combination of sample size and sample proportion, find the margin of error for the 95% confidence level.Use the formula given on page 383.a. n 5 400, p^ 5 .20.b. n 5 400, p^ 5 .80.c. n 5 1000, p^ 5 .50.
Suppose that a margin of error for a sample percentage is reported to be 3%. What is the probability that the difference between the sample percentage and the population percentage will be more than 3%? Interpret the meaning of this probability.
Suppose that a polling organization reports that the margin of error is 4% for a sample survey. Explain what this indicates about the possible difference between a percentage determined from the survey data and the population value of the percentage.
In constructing 99% confidence intervals for proportions, over the long run, about what percentage of the time would each of the following happen?a. The difference between the sample proportion and the population proportion is less than the “Multiplier 3 Standard error.”b. The difference
Refer to Exercise 10.34. Calculate an 80% confidence interval that estimates the proportion of U.S. families with children that always has the television on when they eat dinner as a family?
Refer to Exercise 10.29. Calculate a 50% confidence interval that estimates the proportion of U.S. adults who think penalties for underage drinking should be more strict.
What is the confidence level for a confidence interval computed as Sample proportion 6 3.09 3 Standard error?
What is the confidence level for a confidence interval computed as Sample proportion 6 1.28 3 Standard error?
(p. 382). Then answer part (d).a. 60%.b. 86%.c. 99.8%.d. On the basis of the values of z* found in parts (a)through (c), explain what happens to the width of the confidence interval when the confidence level is increased.
Find z* for each of the confidence levels in parts (a) through(c), and draw a picture similar to Figure
Determine the value of the z* multiplier that would be used to compute an 80% confidence interval for a population proportion.
In a Gallup poll done in 2007, a randomly selected sample of n 5 254 U.S. parents was asked how often the television was on when they ate dinner as a family. About 33% of the sample said “always” (Source: www.pollingreport.com/life.htm).a. Calculate the standard error of the sample
Refer to Exercise 10.20. Calculate a 90% confidence interval for the population proportion who would fire their boss if they could.
(p. 378), in which for a sample of 1003 American adults, .56 was the proportion who think that it is somewhat or very likely that intelligent life exists elsewhere.Compute a 99% confidence interval for the population proportion.
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