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elementary statistics
Just The Essentials Of Elementary Statistics 10th Edition Robert Johnson, Patricia Kuby - Solutions
10.56 Determine the p-value for the following hypothesis tests for the difference between two means with population variances unknown.a. Ha: 1 2 0, n1 6, n2 10, t 1.3b. Ha: 1 2 0, n1 16, n2 9, t2.8c. Ha: 1 2 0, n1 26, n2 16, t 1.8d. Ha: 1 2 5, n1 26,
10.55 Find the value of t for the difference between two means based on an assumption of normality and this information about two samples:Sample Number Mean Std. Dev.1 21 1.66 0.29 2 9 1.43 0.18
10.54 Find the value of t for the difference between two means based on an assumption of normality and this information about two samples:Sample Number Mean Std. Dev.1 18 38.2 14.2 2 25 43.1 10.6
10.53 Calculate the estimate for the standard error of difference between two independent means for each of the following cases:a. s2 1 12, s2 2 15, n1 16, and n2 21b. s2 1 0.054, s2 2 0.087, n1 8, and n2 10c. s1 2.8, s2 6.4, n1 16, and n2 21
10.52 State the null and alternative hypotheses that would be used to test the following claims:a. The difference between the means of the two populations is more than 20 lb.b. The mean of population A is less than 50 more than the mean of population B.c. The difference between the two populations
10.51 State the null and alternative hypotheses that would be used to test the following claims:a. There is a difference between the mean age of employees at two different large companies.b. The mean of population 1 is greater than the mean of population 2.c. The mean yield per county of sunflower
10.50 [EX10-050] At a large university, a mathematics placement exam is administered to all students.Samples of 36 male and 30 female students are randomly selected from this year’s student body and the following scores recorded:Male 72 68 75 82 81 60 75 85 80 70 71 84 68 85 82 80 54 81 86 79 99
10.49 [EX10-049] Approximately 95% of the sunflowers raised in the United States are grown in North Dakota, South Dakota, and Minnesota. To compare yield rates between North and South Dakota, 11 sunflower-producing counties were randomly selected from North Dakota and 14 sunflower-producing
10.48 [EX10-048] “Is the length of a steel bar affected by the heat treatment technique used?” This was the question being tested when the following data were collected.Heat Treatment Lengths (to the nearest inch)1 156 159 151 153 157 159 155 155 151 152 158 154 156 156 157 155 156 159 153 157
10.47 [EX10-047] A study was designed to estimate the difference in diastolic blood pressure readings between men and women. MINITAB was used to construct a 99% confidence interval for the difference between the means based on the following sample data.Males 76 76 74 70 80 68 90 70 90 72 76 80 68
10.46 Part of a testing program on a family of dual bell rockets designed to compensate for low-altitude performance led to two slightly different new designs. The two sets of test flow rates, measured in pounds per second, resulted from testing these two new designs.n x x 2 Design 1 36 278.4
10.45 “Car renters come across steeper rates” (USA Today, May 17, 2005) reported that rates for car rentals are rising but have not surpassed the national average peak of $35.98 a day in 2001. The average national daily rate for the April–June quarter of 2005 was $30.15, yet in some cities,
10.44 A study comparing attitudes toward death was conducted in which organ donors (individuals who had signed organ donor cards) were compared with nondonors. The study is reported in the journal Death Studies. Templer’s Death Anxiety Scale (DAS) was administered to both groups. On this scale,
10.43 Find the 90% confidence interval for the difference between two means based on this information about two samples. Assume independent samples from normal populations.Sample Number Mean Std. Dev.1 20 35 22 2 15 30 16
10.42 Find the confidence coefficient, t df,2, that would be used to find the maximum error for each of the following situations when estimating the difference between two means, 1 2.a. 1 0.95, n1 25, n2 15b. 1 0.98, n1 43, n2 32c. 1 0.99, n1 19, n2 45
10.41 Two independent random samples of sizes 18 and 24 were obtained to make inferences about the difference between two means. What is the number of degrees of freedom? Discuss both cases.
10.40 Two independent random samples resulted in the following:Sample A: nA 24, sA 8.5 Sample B: nB 21, sB 11.3 Find the estimate for the standard error for the difference between two means.
10.39 Two independent random samples resulted in the following:Sample 1: n1 12, s2 1 190 Sample 2: n2 18, s2 2 150 Find the estimate for the standard error for the difference between two means.
10.38 [EX10-038] A research project was undertaken to evaluate two focimeters. Each of 20 lenses of varying powers was read once each on each focimeter. The measurement differences were then calculated, where each difference is Focimeter A Focimeter B. Assume readings are normally
10.37 Referring to Applied Example 10.7:a. What null hypothesis is being tested in each of these 13 tests?b. Why are the “t-calculated” and the “t-critical”values the important values?c. Why is it correct to report their absolute values for both t-values in Table 14?d. What decision is
10.36 [EX10-036] To test the effect of a physical fitness course on one’s physical ability, the number of sit-ups that a person could do in 1 minute, both before and after the course, was recorded. Ten randomly selected participants scored as shown in the following table. Can you conclude that a
10.35 [EX10-035] In reference to the college students who participated in a learning community in Exercise 10.34, a control group of students was also formed for testing and comparison. Ten randomly selected college students, who were not involved in the learning community, were given
10.34 [EX10-034] Ten randomly selected college students, who participated in a learning community, were given pre–self-esteem and post–selfesteem surveys. A learning community is a group of students who take two or more courses together.Typically, each learning community has a theme, and the
10.33 Complete the hypothesis test with alternative hypothesis d 0 based on the paired data that follows and d 0 Y. Use 0.01. Assume normality.Oldest 199 162 174 159 173 Youngest 194 162 167 156 176a. Solve using the p-value approach.b. Solve using the classical approach.
10.32 Use a computer or calculator to complete the hypothesis test with alternative hypothesisd 0 based on the paired data that follow and d M N. Use 0.02. Assume normality.M 58 78 45 38 49 62 N 62 86 42 39 47 68
10.31 Complete the hypothesis test with alternative hypothesis d 0 based on the paired data that follow and d B A. Use 0.05. Assume normality.A 700 830 860 1080 930 B 720 820 890 1100 960a. Solve using the p-value approach.b. Solve using the classical approach.
10.30 [EX10-030] Ten subjects with borderlinehigh cholesterol levels were recruited for a study.The study involved taking a nutrition education class. Cholesterol readings were taken before the class and 3 months after the class.Subject 1 2 3 4 5 6 7 8 9 10 Preclass 295 279 250 235 255 290 310 260
10.29 [EX10-029] Ten people recently diagnosed with diabetes were tested to determine whether an educational program was effective in increasing their knowledge of diabetes. They were given a test, before and after the educational program, concerning self-care aspects of diabetes. The scores on the
10.28 Does a content title help a reader comprehend a piece of writing? Twenty-six participants were given an article to read without a title. They then rated themselves on comprehension of the information on a scale from 1 to 10, where 10 was complete comprehension. The same 26 participants were
10.27 The corrosive effects of various soils on coated and uncoated steel pipe was tested by using a dependent sampling plan. The data collected are summarized by n 40, d 220, d2 6222, where d is the amount of corrosion on the coated portion subtracted from the amount of corrosion on the
10.26 Determine the test criteria that would be used with the classical approach to test the following hypotheses when t is used as the test statistic.a. Ho : d 0 and Ha: d 0, with n 15 and 0.05b. Ho : d 0 and Ha: d 0, with n 25 and 0.05c. Ho : d 0 and Ha: d 0, with n
10.25 Determine the p-value for each hypothesis test for the mean difference.a. Ho : d 0 and Ha: d 0, with n 20 and t 1.86b. Ho : d 0 and Ha: d 0, with n 20 and t1.86c. Ho : d 0 and Ha: d 0, with n 29 and t2.63d. Ho : d 0.75 and Ha: d 0.75, with n 10 and t
10.24 State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test these claims:a. The mean of the differences between the posttest and the pretest scores is greater than 15.b. The mean weight gain, after the change in diet for the laboratory animals, is at least 10
10.23 State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test these claims:a. There is an increase in the mean difference between posttest and pretest scores.b. Following a special training session, it is believed that the mean of the difference in performance
10.22 [EX10-022] In evaluating different measuring instruments, one must first determine whether there is a systematic difference between the instruments. Lenses from several different powers were measured once each by two different instruments. The measurement differences (Instrument A
10.21 [EX10-021] Two men, A and B, who usually commute to work together, decide to conduct an experiment to see whether one route is faster than the other. The men believe that their driving habits are approximately the same, and therefore they decide on the following procedure. Each morning for 2
10.20 [EX10-020] An experiment was designed to estimate the mean difference in weight gain for pigs fed ration A as compared with those fed ration B. Eight pairs of pigs were used. The pigs within each pair were littermates. The rations were assigned at random to the two animals within each pair.
10.19 [EX10-019] Salt-free diets are often prescribed to people with high blood pressure. The following data values were obtained from an experiment designed to estimate the reduction in diastolic blood pressure as a result of consuming a salt-free diet for 2 weeks. Assume diastolic readings to be
10.18 [EX10-018] Use a computer or calculator to find the 95% confidence interval for estimatingd based on these paired data and assuming normality:Before 75 68 40 30 43 65 After 70 69 32 30 39 63
10.17 [EX10-017] Ten subjects with borderlinehigh cholesterol levels were randomly recruited for a study. The study involved taking a nutrition education class. Cholesterol readings were taken before the class and 3 months after the class.Subject 1 2 3 4 5 6 7 8 9 10 Preclass 295 279 250 235 255
10.16 [EX10-016] All students who enroll in a certain memory course are given a pretest before the course begins. At the completion of the course, 10 students are selected at random and given a posttest; their scores are listed here.Student 1 2 3 4 5 6 7 8 9 10 Before 93 86 72 54 92 65 80 81 62 73
10.15a. Find the 95% confidence interval ford given n 26, d 6.3, and sd 5.1.Assume the data are randomly selected from a normal population.b. Compare your interval to the interval found in Example 10.4 (p. 552).
10.14 Find t(15, 0.025). Describe the role this number plays when forming a confidence interval for the mean difference.
10.13 Given this set of paired data:Pairs 1 2 3 4 5 Sample A 3 6 1 4 7 Sample B 2 5 1 2 8 Find:a. The paired differences, d A B, for this set of datab. The mean d of the paired differencesc. The standard deviation sd of the paired differences
10.12 Suppose that 400 students in a certain college are taking elementary statistics this semester.Two samples of size 25 are needed to test some precourse skill against the same skill after the students complete the course.a. Describe how you would obtain your samples if you were to use dependent
10.11 A study is being designed to determine the reasons why adults choose to follow a healthy diet plan. The study will survey 1000 men and 1000 women. Upon completion of the study, the reasons men choose a healthy diet will be compared with the reasons women choose a healthy diet.a. How can the
10.10 An insurance company is concerned that garage A charges more for repair work than garage B charges. It plans to send 25 cars to each garage and obtain separate estimates for the repairs needed for each car.a. How can the company do this and obtain independent samples? Explain in detail.b. How
10.9 Two different types of disc centrifuges are used to measure the particle size in latex paint. A gallon of paint is randomly selected, and 10 specimens are taken from it for testing on each of the centrifuges. There will be two sets of data, 10 data values each, as a result of the testing. Do
10.8 An experiment is designed to study the effect diet has on the uric acid level. The study includes 20 white rats. Ten rats are randomly selected and given a junk-food diet; the other 10 rats receive a high-fiber, low-fat diet. Uric acid levels of the two groups are determined. Do the resulting
10.7 Twenty people were selected to participate in a psychology experiment. They answered a short multiple-choice quiz about their attitudes on a particular subject and then viewed a 45-minute film.The following day the same 20 people were asked to answer a follow-up questionnaire about their
10.6 In trying to estimate the amount of growth that took place in the trees recently planted by the County Parks Commission, 36 trees were randomly selected from the 4000 planted. The heights of these trees were measured and recorded. One year later, another set of 42 trees was randomly selected
10.5 The students at a local high school were assigned to do a project for their statistics class. The project involved having sophomores take a timed test on geometric concepts. The statistics students would then use these data to determine whether there was a difference between male and female
10.4a. Describe how you could select two independent samples from among your classmates to compare the heights of female and male students.b. Describe how you could select two dependent samples from among your classmates to compare their heights as they entered high school with their heights when
10.3 Explain why studies involving identical twins, as in Applied Example 10.3, result in dependent samples of data.
10.1 [EX10-001] Consider the sample data above in Section 10.1.a. What is the population of interest?b. What percentage of each group has their own credit card? How does this compare with the findings reported by the Nellie Mae organization?c. Describe the shape of the distribution you believe
Consider the preceding sample data.a. What is the population parameter of interest?b. Construct a histogram of the data.c. What name would you give to the shape of the histogram in part b?d. Would you say the histogram in part b suggests the variable, amount of time, does not have a normal
Based on the data presented in Section 9.1 for the cardiovascular technicians:a. Find the mean and standard deviation for the amount of time the cardiovascular technicians exercised per week.b. How would you estimate the mean amount of time exercised per week by all cardiovascular technicians?c.
Find:a. t(12, 0.01)b. t(22, 0.025)c. t(50, 0.10)d. t(8, 0.005)
Find:a. t(18, 0.90)b. t(9, 0.99)c. t(35, 0.975)d. t(14, 0.98)
Ninety percent of Student’s t-distribution lies between t1.89 and t 1.89 for how many degrees of freedom?
Ninety percent of Student’s t-distribution lies to the right of t1.37 for how many degrees of freedom?
The variance for each of Student’s t-distributions is equal to df/(df 2). Find the standard deviation for a Student’s t-distribution with each of the following degrees of freedom:a. 10b. 20c. 30 In summary:d. Explain how this verifies Property 5 of the t-distributions listed on p. 476.
In a study of 25 criminals convicted of antitrust offenses, the average age was 54 years, with a standard deviation of 7.5 years. Construct a 90%confidence interval on the true mean age.
A survey of 3000 randomly selected Minnesotans aged 65 and older revealed that, on average, they spent $85 per month on prescription drugs, with a standard deviation of $50.35 per month. Construct a 99% confidence interval for the true mean amount spent per month.
The Robertson square drive screw was invented in 1908, but it has gained in popularity with American woodworkers and home craftspeople only within the last 10 years. The advantages of square drives over conventional screws is indeed remarkable—most notably greater strength, increased holding
[EX09-026] Lunch breaks are often considered too short, and employees frequently develop a habit of “stretching” them. The manager at Giant Mart randomly identified 22 employees and observed the length of their lunch breaks (in minutes)for one randomly selected day during the week:30 24 38 35
[EX09-027] Our modern meat or chicken“broiler” can weigh 5.5 lb at 49 days, a common time to sell the broiler to a meat processor. Before a poultry farmer sells her broilers, she wants to estimate the mean weight of the flock. She selects a random sample of 15 from the current 7-week old
[EX09-028] The addition of a new accelerator is claimed to decrease the drying time of latex paint by more than 4%. Several test samples were conducted with the following percentage decrease in drying time. 5.2 6.4 3.8 6.3 4.1 2.8 3.2 4.7 Assume that the percentage decrease in drying time is
[EX09-029] The pulse rates for 13 adult women were as follows:83 58 70 56 76 64 80 76 70 97 68 78 108 Verify the results shown on the last line of the MINITAB output:MTB TINTERVAL 90 PERCENT CONFIDENCE INTERVAL FOR DATA IN C1 N MEAN STDEV SE MEAN 90% CI C1 13 75.69 14.54 4.03(68.50, 82.88)
Use a computer or calculator to construct a 0.98 confidence interval using the sample data:6 7 12 9 10 8 5 9 7 9 6 5
[EX09-033] The fuel economy information on a new SUV window sticker indicates that its new owner can expect 16 mpg (miles per gallon)in city driving and 20 mpg for highway driving and 18 mpg overall. Accurate gasoline records for one such vehicle were kept, and a random sample of mileage per tank
[EX09-034] College students throw out an average of 640 lb of trash each year, 30% of that in the month before graduation according to the June 2004 Readers Digest article “Campus Castoffs.” Last year, 20 universities raised more than $100,000 for local charities by selling the “junk.” To
Determine the p-value for the following hypothesis tests involving Student’s t-distribution with 10 degrees of freedom.a. Ho : 15.5, Ha: 15.5, t2.01b. Ho : 15.5, Ha: 15.5, t 2.01c. Ho : 15.5, Ha: 15.5, t 2.01d. Ho : 15.5, Ha: 15.5, t2.01
Determine the critical region and critical value(s) that would be used in the classical approach to test the following null hypotheses:a. Ho : 10, Ha: 10 ( 0.05, n 15)b. Ho : 37.2, Ha: 37.2( 0.01, n 25)c. Ho: 20.5, Ha: 20.5 ( 0.05, n 18)d. Ho : 32.0, Ha:
Use a computer or calculator to find the p-value for the hypothesis test: Ho : 32, Ha: 32, n 16, x 32.93, s 3.1.
Use both the p-value and classical approaches to hypothesis testing to reach a decision for each of the following situations. Use 0.05.a. Ho : 128, Ha: 128, n 15, t 1.60b. Ho : 18, Ha: 18, n 25, t 2.16c. Ho : 38, Ha: 38, n 45, t1.73d. Compare the results
In reference to Applied Example 9.7(p. 487):a. Verify that t(44) 1.92 is significant at the 0.05 level.b. Verify that t(44) 3.41 is significant at the 0.01 level.c. Explain why t(44) 1.81, p .10, makes sense only if the hypothesis test is two-tailed.d. If the test is one-tailed, what level
A student group maintains that each day, the average student must travel for at least 25 minutes one way to reach college. The college admissions office obtained a random sample of 31 one-way travel times from students. The sample had a mean of 19.4 minutes and a standard deviation of 9.6 minutes.
Consumers enjoy the deep selection of merchandise made possible by specialty stores that sacrifice breadth for greater depth. Consider stores that carry only Levi Strauss pants. The company reports that a fully stocked Levi’s store carries 130 ready-to-wear pairs of jeans for any given waist and
Up all night? Caffeine crave may cause longterm health problems. Homework, jobs, and studying all may be causes for teens to consume too much coffee in their everyday lives. Health officials warn that high caffeine intake is not good for anyone, but coffee drinking continues to become more and more
[EX09-051] To test the null hypothesis “the mean weight for adult males equals 160 lb” against the alternative “the mean weight for adult males exceeds 160 lb,” the weights of 16 males were obtained:173 178 145 146 157 175 173 137 152 171 163 170 135 159 199 131 Assume normality and verify
[EX09-053] Use a computer or calculator to complete the hypothesis test: Ho : 52, Ha: 52, 0.01 using the data:45 47 46 58 59 49 46 54 53 52 47 41
[EX09-054] The recommended number of hours of sleep per night is 8 hours, but everybody“knows” that the average college student sleeps less than 7 hours. The number of hours slept last night by 10 randomly selected college students is listed here: 5.2 6.8 6.2 5.5 7.8 5.8 7.1 8.1 6.9 5.6 Use a
[EX02-182] Gasoline pumped from a supplier’s pipeline is supposed to have an octane rating of 87.5. On 13 consecutive days, a sample was taken and analyzed with the following results. 88.6 86.4 87.2 88.4 87.2 87.6 86.8 86.1 87.4 87.3 86.4 86.6 87.1a. If the octane ratings have a normal
[EX09-057] The density of the earth relative to the density of water is known to be 5.517 g/cm3.Henry Cavendish, an English chemist and physicist(1731–1810), was the first scientist to accurately measure the density of the earth. Following are 29 measurements taken by Cavendish in 1798 using a
Acetaminophen is an active ingredient found in more than 600 over-the-counter and prescription medicines, such as pain relievers, cough suppressants, and cold medications. It is safe and effective when used correctly, but taking too much can lead to liver damage.Source:
[EX09-060] A winemaker has placed a large order for the no. 9 corks described in Applied Example 6.15(p. 330) and is concerned about the number of corks that might have smaller diameters.During the corking process, the corks are squeezed down to 16 to 17 mm in diameter for insertion into bottles
[EX09-061] Length is not very important in evaluating the quality of corks because it has little to do with the effectiveness of a cork in preserving wine. Winemakers have several lengths to choose from and order the length cork they prefer (long corks tend to make a louder pop when the bottle is
Of the 150 elements in a random sample, 45 are classified as “success.”a. Explain why x and n are assigned the values 45 and 150, respectively.b. Determine the value of p . Explain how p is found and the meaning of p .For each of the following situations, find p .c. x 24 and n 250d. x 640
Show that Vnpa pq simplifies to n n
Find , the area of one tail, and the confidence coefficients of z that are used with each of the following levels of confidence.a. 1 0.90b. 1 0.95c. 1 0.99
Find , the area of one tail, and the confidence coefficients of z that are used with each of the following levels of confidence.a. 1 0.80b. 1 0.98c. 1 0.75
Refer back to Example 9.8. Another sample is taken to estimate the proportion of students who drive convertibles. Results are n 400 and x 92.Find:a. The estimate for the standard errorb. The 95% confidence interval
“You say tomato, burger lovers say ketchup!”According to a recent T.G.I. Friday’s restaurants’random survey of 1027 Americans, approximately half (47%) say that ketchup is their preferred burger condiment. The survey quoted a margin of error of plus or minus 3.1%.Source: Harris
Although most people are aware of minor dehydration symptoms such as dry skin and headaches, many are less knowledgeable about the causes of dehydration. According to a poll done for the Nutrition Information Center, the results of a random sample of 3003 American adults showed that 20% did not
In a sample of 60 randomly selected students, only 22 favored the amount being budgeted for next year’s intramural and interscholastic sports.Construct the 99% confidence interval for the proportion of all students who support the proposed budget amount.
The December 21, 2004, USA Today article“On the Path to Problem Gambling: National Survey Shows Casinos, Slots and Lotteries Attract Youth Into Potentially Addictive Habit” reported on a poll of 200 male and 199 female teenagers, aged 14 to 17. The findings reported were that 66% of the male
Of the 1742 managers and professionals polled by Management Recruiters International, May 2002, 27.8% work late 5 days a week on average.Using a 99% confidence interval for the true binomial proportion based on a random sample of 1742 binomial trials and an observed proportion of 0.278, estimate
New research suggests that children often learn coping skills from imaginary friends. In a study of 100 children done at the University of Oregon and reported in Developmental Psychology(USA Today, December 20, 2004, “‘Pretend’ friends, actual benefits”), 33% of the children still had an
Construct 90% confidence intervals for the binomial parameter p for each of the following pairs of values. Write your answers on the chart.f. Explain the relationship between the answers to parts a and b.g. Explain the relationship between the answers to parts c–e. Observed Proportion p' = xln
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