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

Refer to Exercise 13.14, part (a), which posed the following research question: “Many cars have a recommended tire pressure of 32 psi (pounds per square inch). At a roadside vehicle safety checkpoint, officials plan to randomly select 50 cars for which this is the recommended tire pressure and
A cell phone company knows that the mean length of calls for all of its customers in a certain city is 9.2 minutes. The company is thinking about offering a senior discount to attract new customers, but first wants to know whether or not the mean length of calls for current customers who are
It has been hypothesized that the mean pulse rate for college students is about 72 beats per minute. A sample of Penn State students recorded their sex and pulse rate. Assume that the sample is representative of all Penn State men and women for pulse rate measurements. The summary statistics follow:
Suppose that a study is done to test the null hypothesis H0: m 5 100. A random sample of n 5 50 observations results in x 5 102 and s 5 15.a. What is the null standard error in this case?b. Plug numbers into the formula t 5 Sample statistic 2 Null value Null standard errorc. On the basis of the
◆ The dataset cholest on the companion website includes cholesterol levels for heart attack patients and for a group of control patients. It is recommended that people try to keep their cholesterol level below 200. The following Minitab output is for the control patients:
Use Table A.2 to find the critical value and rejection region in each of the following situations. Then determine whether the null hypothesis would be rejected. In each case the null hypothesis is H0: m 5 50.a. Ha: m . 50, n 5 10, a 5 .05, test statistic t 5 1.95.b. Ha: m , 50, n 5 10, a 5 .05,
Use Table A.2 to find the critical value and rejection region in each of the following situations. Then determine whether the null hypothesis would be rejected. In each case, the null hypothesis is H0: m 5 100.a. Ha: m . 100, n 5 21, a 5 .05, test statistic t 5 2.30.b. Ha: m . 100, n 5 21, a 5 .01,
Find the p-value and draw a sketch showing the p-value area for each of the following situations in which the value of t is the test statistic for the hypotheses given:a. H0: m 5 m0, Ha: m 2 m0, n 5 81, t 5 2.00.b. H0: m 5 m0, Ha: m 2 m0, n 5 81, t 5 22.00.
Find the p-value and draw a sketch showing the p-value area for each of the following situations in which the value of t is the test statistic for the hypotheses given:a. H0: m 5 m0, Ha: m . m0, n 5 28, t 5 2.00.b. H0: m 5 m0, Ha: m . m0, n 5 28, t 5 22.00.
Give the value of the test statistic t in each of the following situations.a. H0: m 5 50, x 5 60, s 5 90, n 5 100.b. Null value 5 100, sample mean 5 98, s 5 15, sample size 5 40.13.17. Give the value of the test statistic t for a test with H0: m 5 250, x 5 270, standard error 5 5 and n 5 100.
Define the parameter of interest, and then use it to write the null and alternative hypotheses (in symbols) for the following situation. Nonprofit hospitals must provide a certain amount of charity care to maintain nonprofit, tax-exempt status. Although the amount differs by area, let’s suppose
Define the parameter of interest, and then use it to write the null and alternative hypotheses (in symbols) for each of the following research questions.a. Many cars have a recommended tire pressure of 32 psi(pounds per square inch). At a roadside vehicle safety checkpoint, officials plan to
Review the five steps for any hypothesis test. Can any of the five steps be done before collecting the data?Explain.
If you were given a set of data for which the question of interest was about the population mean, explain how you would determine whether it would be valid to do a onesample t-test using that set of data.
Explain why each of the following terms is used for the procedure outlined in Section 13.1.a. Hypothesis testing.b. Significance testing
Explain why the null hypothesis for a significance test is rejected when the p-value is small rather than when it is large.
Explain why a “standardized statistic” is used in hypothesis testing, instead of simply using the difference between the sample statistic and the null value as the test statistic.
Refer to Exercises 13.4 and 13.6. Specify the null value that the researchers are interested in testing, and write the null hypothesis using the appropriate symbol(s) for the parameter of interest. If you haven’t already done so in Exercise 13.6, make sure that you specify the population(s) to
Refer to Exercises 13.3 and 13.5. Specify the null value that the researchers are interested in testing, and write the null hypothesis using the appropriate symbol(s) for the parameter of interest. If you haven’t already done so in Exercise 13.5, make sure that you specify the population(s) to
Refer to Exercise 13.4. For each part, write and define the notation that would be used for the population parameter of interest. Make sure that you specify the population(s) to which the parameter applies.
Refer to Exercise 13.3. For each part, write and define the notation that would be used for the population parameter of interest. Make sure that you specify the population(s) to which the parameter applies.
For each of the following research questions, specify whether the parameter of interest is one population mean, the population mean of paired differences, or the difference between the means of two populations.
For each of the following research questions, specify whether the parameter of interest is one population mean, the population mean of paired differences, or the difference between the means of two populations.a. Nutrition trends have changed over the years, and this may affect growth. Researchers
Explain whether each of the following statements is true.a. Hypotheses and conclusions from hypothesis testing apply only to the samples on which they are based.b. The p-value is calculated with the assumption that the null hypothesis is true.
Explain whether each of the following statements is true.a. One of the two possible conclusions in hypothesis testing is to accept the null hypothesis.b. The statements “reject the null hypothesis” and “accept the alternative hypothesis” are equivalent.
For this exercise, use the dataset UCDavis2 on the companion website. The variable Seat is a response to the question,“Where do you typically sit in a classroom?” Possible responses were F 5 Front, M 5 Middle, B 5 Back.a. Test the hypothesis that a majority of students prefer to sit in the
The dataset GSS-08 on the companion website includes information on sex and on whether or not respondents think marijuana should be legal (marijuan). Use the dataset to test the hypothesis that the proportions of males and females who thought marijuana should be legal differed for the 2008
For this exercise, use the dataset UCDavis2 on the companion website. The variable Friends is a response to the question, “Who do you find it easiest to make friends with?People of the (circle one) Same Sex or Opposite Sex?” The responses are S 5 same or O 5 opposite.a. Is there sufficient
Refer to Exercise 12.113. A Gallup poll the previous August(1999) asked n 5 1028 U.S. adults the same question, and 524 responded that they were somewhat or completely dissatisfied.a. Repeat the test in Exercise 12.113 and make a conclusion for August 1999.b. Referring to the data presented in
Refer to Figure 12.1 on page 463. Explain what probabilities can be assigned to each of the following, and whether they are conditional probabilities or not.
A Gallup poll taken in August 2000 (Chambers, 2000) asked U.S. adults in a random sample of n 5 1019 about their satisfaction with K-12 education. One question was: “Overall, how satisfied are you with the quality of education students receive in grades kindergarten through grade twelve in the
Refer to Exercise 12.111. The authors also wanted to test whether women with different levels of education would differ in their ability to guess the sex of their babies correctly. Of the n 5 45 women with more than 12 years of education, 32 guessed correctly. Of the n 5 57 women with 12 or fewer
Perry et al. (1999) wanted to test the folklore that women who have not been given information about the sex of their unborn child can guess it at better than chance levels. They asked a sample of 104 pregnant women to guess the sex of their babies, and 57 guessed correctly. Assuming chance
Refer to Exercise 12.109. The test showed that the difference in proportions that had heart attacks after taking aspirin and after taking a placebo was highly statistically significant.Suppose that the study had 2200 participants instead of over 22,000, but that the proportions having heart attacks
Case Study 1.6 presented data on 22,071 physicians who were randomly assigned to take aspirin or a placebo every other day for five years. Of the 11,037 taking aspirin, 104 had a heart attack, while of the 11,034 taking placebo, 189 had a heart attack.
Refer to Example 12.17 (pp. 476 and 478), comparing the proportion of children with ear infections while taking xylitol or a placebo. Read the discussion of Type 1 and Type 2 errors, and explain the consequences of each type of error if it were to have been made in this study.
A Gallup poll taken on a random sample of Canadian adults in February 2000 asked the question, “Do you favour or oppose marriages between people of the same sex?” A similar poll was taken in April 1999 (Edwards and Mazzuca, 2000).The Minitab output for the “two proportions” procedure(with
Refer to Example 12.11 (p. 466), in which convincing evidence was found for the importance of order in a “random”selection between two letters. Suppose that a student in your class ran for president of the campus student association and lost. After reading Example 12.11, she realized that
Refer to Exercise 12.103. Some students were asked if they preferred C or P, while other students were asked if they preferred P or C. Of the 159 respondents, 86 responded with the first drink presented. Test the hypothesis that the first
According to USA Today (Snapshot, April 20, 1998, also referenced in Exercise 9.143), a random sample of 8709 adults taken in 1976 found that 9% believed in reincarnation. A poll of 1000 adults in 1997 found that 25% believed in reincarnation. Test the hypothesis that the proportion of adults
In a survey of students at the University of California, Davis(UCD), students were asked which of two popular soft drinks they preferred—let’s call them brand C and brand P.Of the 159 respondents, 80 preferred brand P and 79 preferred brand C. Assuming that these students represent all students
A professor planned to give an examination in a large class on the Monday before Thanksgiving vacation. Some students asked whether he could change the date because so many of their classmates had at least one other exam on that date. They speculated that at least 40% of the class had this problem.
◆ In Chapter 2, we saw data from a statistics class activity in which students were asked to “randomly” pick a number(integer) from 1 to 10. Of the 190 students, 56 picked the number 7. Carry out the five steps of hypothesis testing to determine if people similar to these students are more
For a test of H0: p 5 .25 versus Ha: p . .25, for what range of values of the sample proportion p^ will the p-value for the test be greater than .5? Explain your answer.
For a one-sided hypothesis test for a proportion in which the alternative hypothesis is Ha: p , p0, for what values of the test statistic z will the p-value be greater than .5? Explain your answer.
Refer to Exercise 12.97. For each of the two situations described, explain the consequences of a Type 1 error and the consequences of a Type 2 error. For part (a), explain which type would be more serious for the patients, and for part (b)explain which type would be more serious for the student who
For the following two situations, define the population parameter in words. Then specify the null and alternative hypotheses in symbols.a. For people suffering from a certain type of chronic pain, 70% experience temporary relief when they take a standard medication. If a new medication appears to
Specify the null and alternative hypotheses in words for each of the following research questions.a. Does listening to Mozart increase performance on an intelligence test?b. Does talking to plants result in better growth for the plants?c. Does drinking fluoridated water lead to increased bone
Max likes to keep track of birthdays of people he meets. He has 170 birthdays listed on his birthday calendar. One cold January night, he comes up with the theory that people are more likely to be born in October than they would be if all 365 days were equally likely. He consults his birthday
Give an example of a possible hypothesis of interest about a population proportion. Be sure to specify the population and the population parameter that the hypothesis is about.
Give an example of a possible hypothesis of interest about the difference between two population proportions. Be sure to specify the populations and the population parameter the hypothesis is about.
Refer to the five steps in any hypothesis test listed in Section 12.1. Only one of the steps can be performed before the data are collected. Which step is it?
In a survey of 240 students in an elementary statistics class at the University of California-Davis (UCD), 20 said that they were left-handed and 220 said that they were right-handed.Assume that the students are representative of all students at the school. Does this provide evidence that the
A student has been accused of cheating on an examination by copying another student’s paper, and you have been asked to serve on the panel that must decide the student’s fate. If the student is found guilty, he will fail the course and will have to write an essay on honesty for the school
This is also Exercise 1.17. A randomized experiment was done in which overweight men were randomly assigned to either exercise or go on a diet for a year. At the end of the study there was a statistically significant difference in average weight loss for the two groups. What additional information
Consider the two conditions necessary for conducting a z-test for a proportion. One is a sample size condition, and the other is a condition about how the sample was collected.For each of the two conditions, explain why it is required in order for the test and the results to be valid.
Refer to the five steps of any hypothesis test, given in Section 12.1. Which step(s) are different if the rejection region approach is used instead of the p-value approach?
Refer to Case Study 1.6, comparing heart attack rates for men who had taken aspirin or a placebo. Suppose that the observed proportions of .017 and .0094 are actually the correct population proportions who would have heart attacks with a placebo and with aspirin. The following Minitab output shows
Minitab can provide power for a variety of situations. Suppose that a test for ESP has four choices, and that the probability of a correct guess by chance on each trial is .25. A researcher believes that the true probability of a correct guess is .33. The following output shows the power of the
Suppose that a study is designed to choose between the following hypotheses:Null hypothesis: Population proportion is .20.Alternative hypothesis: Population proportion is higher than .20.On the basis of a random sample of size 400, the sample proportion is .25.a. Compute the z-score corresponding
An advertisement for Claritin, a drug for seasonal nasal allergies, made this claim: “Clear relief without drowsiness.In studies, the incidence of drowsiness was similar to placebo” (Time, February 6, 1995, p. 43). The advertisement also reported that 8% of the 1926 Claritin takers and 6% of
Which do you think is more informative when you are given the results of a study, a confidence interval or a p-value?Explain.
Suppose you were to read that a new study based on 100 men had found that there was no difference in heart attack rates for men who exercised regularly and men who did not. Do you think the study found exactly the same rate of heart attacks for the two groups of men? In the context of the material
In reporting the results of a study, explain why a distinction should be made between “statistical significance” and “significance” as the term is used in ordinary language.
Which do you think is more informative when you are given the results of a hypothesis test — the p-value or the decision about whether to reject the null hypothesis? Explain.
One possible problem in hypothesis testing is that researchers fail to find a statistically significant result even though the null hypothesis is false. Is this problem more likely to occur with a very small sample or with a very large sample?Explain.
Researchers know that 20% of a certain ethnic group has a distinctive trait. They want to know whether the proportion with the trait is higher in a second ethnic group. They take a random sample of n members of the second group and find the sample proportion p^ with the trait. The parameter of
Sometimes a result that is statistically significant does not have practical significance. Is this more likely to happen when the sample size is very large or when it is very small?Explain.
Refer to Exercise 12.74. In each case, suppose the sample proportion is p^ 5 .75 and compute the test statistic z and the p-value. Then make a conclusion using a .05 level of significance. Comment on the relationship between the sample size and the conclusions.
Suppose that the null and alternative hypotheses in a test are as follows:H0: p 5 .70 Ha: p ≠ .70
Exercise 4.11. described a case–control study comparing short to not-short English secondary school students. Of n 5 92 short students, 42 said they had been bullied in school. Of n 5 117 not-short students, 30 said they had been bullied in school. Here is Minitab output for comparing two
The headline for an article in the Sacramento Bee read,“Women appear to be better investors than men in study”(Jack Sirard, April 24, 2005, p. D1). The conclusion was based on a telephone poll of 500 men and 500 women.One quote in the article was “men are much more likely to stick with a
Case Study 10.3 (p. 392) reported on a survey of Penn State students asking the question, “Would you date someone with a great personality even though you did not find them attractive?” Of the n 5 131 women, 61.1% said yes, and of the n 5 61 men, 42.6% said yes. Is there sufficient evidence to
Refer to Exercise 12.69. The same poll asked the question,“Which of the following do you think is the primary cause of gun violence in America—the availability of guns, the way parents raise their children, or the influences of popular culture such as movies, television, and the Internet?”
A Gallup poll taken in May 2000 asked the question, “In general, do you feel that the laws covering the sale of firearms should be made: more strict, less strict, or kept as they are now?” Of the n 5 493 men who responded, 52% said“more strict,” while of the n 5 538 women who responded, 72%
Exercise 10.85 presented a table in which men were classified according to whether or not they had a pierced ear and a tattoo. Of the 424 men with no pierced ear, 43 had a tattoo.Of the 141 men with at least one pierced ear, 42 had a tattoo.Assuming that these men are a random sample of college
presented results of a survey asking college students whether they would return the money if they found a wallet on the street. Of the 93 women, 84 said they would, and of the 75 men, 53 said they would. Assume that these students represent all college students. Test the null hypothesis that equal
◆ Exercise
Exercises 4.10 and 4.69 presented data on grumpy old men and heart disease. In Chapter 4, the goal was to determine if there was a relationship between the two variables. A onetailed test may also make sense. We might hypothesize that if there is a difference in the probability of developing heart
Is the proportion of men who write a shopping list before going shopping less than the proportion of women who do so?Let p1 and p2 represent the population proportions of men and women, respectively, who use shopping lists. Suppose that a random sample of 50 men and 50 women were asked if they use
and to the discussion of the rejection region approach to hypothesis testing (for z-tests) in Section 12.2. In each part (a and b), find the rejection region that would be used for a 5 .05, and then state a conclusion for the z-statistic given.
Refer to Exercise
State a conclusion for each of the following situations, using a 5 .05:a. H0: p1 2 p2 5 0, Ha: p1 2 p2 , 0; z 5 21.99.b. H0: p1 2 p2 5 0, Ha: p1 2 p2 . 0; z 5 1.78.
State a conclusion for each of the following situations, using a 5 .05:a. H0: p1 2 p2 5 0, Ha: p1 2 p2 , 0; z 5 0.33.b. H0: p1 2 p2 5 0, Ha: p1 2 p2 . 0; z 5 0.33.
Find the p-value and draw a sketch of the p-value area for each of the following situations in which the value of z is the test statistic for the hypotheses given:a. H0: p1 2 p2 5 0, Ha: p1 2 p2 . 0; z 5 1.75.b. H0: p1 2 p2 5 0, Ha: p1 2 p2 . 0; z 5 21.75.
Find the p-value and draw a sketch of the p-value area for each of the following situations in which the value of z is the test statistic for the hypotheses given:
(Computer software or calculator is required.) Refer to Exercise 12.57.a. What is the exact p-value for that situation?b. What conclusion can be made about the hypotheses?Explain.
(Computer software or calculator is required.) A multiplechoice test consists of 15 questions with four choices each.The teacher wants to test the hypothesis that a student is just guessing versus the hypothesis that the probability of a correct answer on each question is higher than it would be if
Describe how to find the exact p-value in a test of H0: p 5 .25 versus Ha: p . .25 when the sample size is n 5 50 and we have observed X 5 17 successes. What probability distribution should be used? What is the interval of possible X values for which a probability must be found?
Describe how to find the exact p-value in each of the following situations. What probability distribution should be used? What is the interval of possible X values for which a probability must be found?a. H0: p 5 .25; Ha: p , .25; n 5 50; X 5 17 successes.b. H0: p 5 .5; Ha: p ≠ .5; n 5 50; X 5 17
A Gallup poll released on October 13, 2000 (Chambers, 2000) found that 47% of the 1052 U.S. adults surveyed classified themselves as “very happy” when given the choices of“very happy,” “fairly happy,” or “not too happy.” Suppose that a journalist who is a pessimist took advantage of
In Example 12.13 (p. 469), results were given for a survey of students in a statistics class who measured the lengths of their right and left feet to the nearest millimeter. The right and left foot measurements were equal for 103 of the 215 students. Assuming that this class is representative of
Suppose that a two-sided test for a proportion resulted in a p-value of .07.a. Using the usual a 5 .05 criterion for hypothesis testing, would we conclude that the population proportion was different from the null hypothesis value? Explain.b. Suppose that the test had been constructed as a onesided
Suppose that a one-sided test for a proportion resulted in a p-value of .04. What would the p-value be if the test was two-sided instead?
Time magazine reported that in a 1994 survey of 507 randomly selected adult American Catholics, 59% answered yes to the question “Do you favor allowing women to be priests?”(Time, 26 December–2 January 1995, pp. 74 –76).a. Set up the null and alternative hypotheses for deciding whether more
In Exercise 12.25, we described a survey done to determine whether artists are more likely to be left-handed than others in the general population. If we use p to represent the proportion of all artists who are left-handed, the hypotheses are H0: p 5 .10 and Ha: p . .10. The sample result was that
Explain the difference between the null standard error used in the denominator of a z-statistic for a test for a proportion and the standard error used in finding a confidence interval for a proportion.
Refer to Exercise 12.47. In each case, calculate the p-value for the test.
For each of the following, calculate the z-statistic:a. Sample size n 5 500; sample proportion p^ 5 .30.H0: p 5 .20 Ha: p . .20b. Sample size n 5 200; sample proportion p^ 5 .50.H0: p 5 .80 Ha: p , .80
For each of the following, calculate the z-statistic:a. Sample size n 5 30; sample proportion p^ 5 .60.H0: p 5 .50 Ha: p ≠ .50b. Sample size n 5 60; sample proportion p^ 5 .10.H0: p 5 .25 Ha: p , .25

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