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Statistics Principles And Methods 7th Edition Richard A. Johnson, Gouri K. Bhattacharyya - Solutions

A person with asthma took measurements by blowing into a peak-flow meter on seven consecutive days.(a) Obtain a 95% confidence interval for the population mean peak-flow. (b) Conduct an a = .10 level test of H0: Î¼ = 453 versus H1: Î¼ ‰ 453.
Times to finish a sixteen ounce bottle of mayonnaise, were recorded by a sample of 11 purchasers. It is determined that ∑xi = 645.7 days and ∑(xi - )2 = 198.41. (a) Obtain a point estimate of the population mean life μ and its 90% error margin. (b) Obtain a 95% confidence interval for the
Using the table of percentage points of the x2 distributions, find: (a) x2.05s with d.f. = 6. (b) x2.025 with df- = 22. (c) The lower .05 point with d.f. = 6. (d) The lower .025 point with d.f. = 22.
Using the table for the f distributions, make an assessment for the probability of the stated event. (a) T > 1.9 when d.f. = 16. (b) T < -1.5 when d.f. = 11. (c) |T| > 1.9 when d.f. = 10. (d) |T| < 2.8 when d.f. = 17.
Using the table for the x2 distributions, find: (a) The 90th percentile of x2 when d.f. = 11. (b) The 10th percentile of x2 when d.f. = 8. (c) The median of x2 when d.f. = 23. (d) The 1st percentile of x2 when d.f. = 40.
Refer to Exercise 9.68. Conduct a test of hypothesis with the intent of establishing that the mean bottle life is different from 55.0 days.(a) Formulate the null and alternative hypotheses.(b) Determine the test statistic.(c) Give the form of the rejection region.(d) What is the conclusion to your
Refer to the data of Exercise 9.66. Is there strong evidence that the standard deviation for the efficiency of the new model is below .30?
Refer to the water quality data in Example 4. Perform a test of hypotheses with the intent of showing that the population standard deviation is less than 18.0. Take α = .05.
Refer to the data on the head length (cm) of male grizzly bears given in Table D.6 of the Data Bank. A computer calculation for a test of H0: Î¼ = 21 versus H1: Î¼ ‰ 21 is given below.(a) What is the conclusion if you test with Î± = .01? (b) What
Refer to the computer output concerning the head length (cm) of male grizzly bears in Exercise 9.74. (a) Is the population mean head length for all male bears in the study area contained in this interval? (b) Explain why you are 95% confident that it is contained in the interval.
Refer to the data on the length (cm) of male grizzly bears given in Table D.6 of the Data Bank. (a) Find a 99% confidence interval for the population mean. (b) Is the population mean length for all male grizzly bears in Alaska contained in this interval? (c) Explain why you are 99% confident that
Refer to the computer anxiety scores (CARS) for males in Table D.4 of the Data Bank. Conduct an α = .025 level of H0: μ = 2.7 versus H1: μ > 2.7.
Researchers3 asked participants to carry a counting device for one week and to record the number of times they thought about food each day. The average of the seven counts is intended to represent a typical day. For 19 males, we havetimes per day. (a) Make a graphical summary, for instance a dot
What can you say about the number c in each case? Justify your answer. (a) P[T > c] = .016 when d.f. = 11. (b) P[T < -c] = .004 when d.f. = 13. (c) P [|T| > c = .03 when d.f. = 6. (d) P [|T| < c] = .96 when d.f. = 27.
The weights from a random sample of 20 golden retriever dogs have mean 76.1 pounds and standard deviation 5.9 pounds. Assume that the weights of the dogs have a normal distribution. (a) Construct a 98% confidence interval for the population mean. (b) What is the length of this confidence interval?
Grades for first semester are compared to those for second semester. The five one-semester courses biology, chemistry, English, history, and psychology must be taken next year. Make a list of all possible ways to split the courses into two groups where the first group has two courses to be taken
A linguist wants to compare the writing styles in two magazines and one measure is the number of words per sentence. On the basis of 50 randomly selected sentences from each source, she finds Magazine 1 n1 = 50 = 12.6 s1 = 4.2 Magazine 2 n2 = 50 = 9.5 s2 = 1.9 Determine a 98% confidence
Refer to Exercise 10.10. Perform a test of hypothesis that is intended to show that the mean for magazine 1 is more than 2 words larger than the mean for magazine 2. (a) Formulate the null and alternative hypotheses. (Define any symbols you use.) (b) State the test statistic and the rejection
Refer to Example 4. Workers in three occupations were questioned about satisfaction with their jobs. Suppose the number of responses in each of the four categories areAssign 1 to very dissatisfied, 2 to a little dissatisfied, 3 to moderately satisfied, and 4 to very satisfied. (These data have
Refer to the confidence interval obtained in Exercise 10.12(b). If you were to test the null hypothesis that the mean satisfaction scores are equal versus the two-sided alternatives, what would be the conclusion of your test with a = .05? (See Section 3 of Chapter 9.)
In a study of interposal aggression and its possible effect on child behavior, the behavior problem checklist (BPC) scores were recorded for 47 children whose parents were classified as aggressive. The sample mean and standard deviation were 7.92 and 3.45, respectively. For a sample of 38 children
An experiment was conducted to study the effect of eating walnuts on the quality of sperm.2 The subjects were healthy men 21-35 years old. The treatment group received 75 gm of whole-shelled walnuts a day for 12 weeks. This was a single blind trial where the assessors of sperm quality were not told
Referring to the data in Exercise 10.15, determine a 99% confidence interval for the difference of mean change.
Psychologists have made extensive studies on the relationship between child abuse and later criminal behavior. Consider a study that consisted of the follow-ups of 52 boys who were abused in their preschool years and 67 boys who were not abused. The data of the number of criminal offenses of those
The generic output below summarizes the data, given in Table D.5 of the Data Bank, on the pretest percent body fat in male and female students.Find a 99% confidence interval for the difference of mean percent body fat.
Suppose that measurements of the size of butterfly wings (cm) for two related species yielded the data(a) Calculate s2pooled; (b) Give an estimate of the common standard deviation for the number of uses. (c) Evaluate the t statistic for testing equality of the two population mean number of uses.
Six mice-Alpha, Tau, Omega, Pi, Beta, and Phi-are to serve as subjects. List all possible ways to split them into two groups with the first having 4 mice and the second 2 mice.
Three male and three female students recorded the number of times they used a credit card in one week.(a) Calculate s2pooled; (b) Give an estimate of the common standard deviation for the wing size for the two species. (c) Evaluate the t statistic for testing equality of the two population mean
Two gel pens, Gel-1 and Gel-2, are compared on the basis of the number of weeks before they stop writing. Out of 27 persons available, 13 are randomly chosen to receive Gel-1 and the other 14 receive Gel-2. These are the only pens they use for writing.(a) Obtains s2pooled. (b) Test H0:
The data on the weight (lb) of male and female wolves, from Table D.9 of the Data Bank, are(a) Test the null hypothesis that the mean weights of males and females are equal versus a two-sided alternative. Take Î± = .05. (b) Obtain a 95% confidence interval for the difference of
To compare two programs for training industrial workers to perform a skilled job, 20 workers are included in an experiment. Of these, 10 are selected at random and trained by method 1; the remaining 10 workers are trained by method 2. After completion of training, all the workers are subjected to a
Does the shape of the glass influence how fast a person drinks? As part of a larger study, some participants drank lager from a 12-ounce glass that was either curved or had straight sides. To distract them, they were told their task was to find words in a puzzle but they were videoed and the times
Given here are the sample sizes and the sample standard deviations for independent random samples from two populations. For each case, state which of the three tests you would use in testing hypotheses about μ1, - μ2: (l) Z test, (2) t test with pooling, (3) approximate t test without pooling.
To compare the effectiveness of isometric and isotonic exercise methods, 20 obese male students are included in an experiment: 10 are selected at random and assigned to one exercise method; the remaining 10 are assigned to the other exercise method. After five weeks, the reductions in abdomen
Refer to Exercise 10.26. (a) Aside from the type of exercise method, identify a few other factors that are likely to have an important effect on the amount of reduction accomplished in a five-week period. (b) If you were to design this experiment, describe how you would divide the 20 students into
Refer to Exercise 10.25 (c). In addition, = 21.1 and = 15.4. Test H0: μ1, - μ2 = 0 versus H1: μ1 - μ2 < 0 at level α = .05.
Six students in a psychology course have volunteered to serve as subjects in a matched pairs experiment.(a) List all possible sets of pairings if subjects are paired by age.(b) If subjects are paired by gender, how many pairs are available for the experiment?
Early studies showed a disproportionate number of heavy smokers among lung cancer patients. One scientist theorized that the presence of a particular gene could tend to make a person want to smoke and be susceptible to lung cancer. (a) How would randomization settle this question? (b) Would such a
Observations on 10 mothers who nursed their babies and 8 who did not revealed that nursing mothers felt warmer toward their babies. Can we conclude that nursing affects a mother's feelings toward her child?
Suppose that you are asked to design an experiment to study the effect of a hormone injection on the weight gain of pregnant rats during gestation. You have decided to inject 6 of the 12 rats available for the experiment and retain the other 6 as controls. (a) Briefly explain why it is important to
Given the following matched pairs sample,x y6................... 34................... 18................... 36................... 59................... 76................... 8(a) Evaluate the f statistic(b) How many degrees of freedom does this f have?
Two sun blockers are to be compared. One blocker is rubbed on one side of a subject's back and the other blocker is rubbed on the other side. Each subject then lies in the sun for two hours. After waiting an additional hour, each side is rated according to redness.(a) Evaluate the t statistic(b)
It is claimed that an industrial safety program is effective in reducing the loss of working hours due to factory accidents. The following data are collected concerning the weekly loss of working hours due to accidents in six plants both before and after the safety program is instituted.Do the data
A manufacturer claims his boot waterproofing is better than the major brand. Five pairs of shoes are available for a test. (a) Explain how you would conduct a paired sample test. (b) Write down your assignment of waterproofing to each shoe. How did you randomize?
A food scientist wants to study whether quality differences exist between yogurt made from skim milk with and without the pre culture of a particular type of bacteria, called Psychrotrops (PC). Samples of skim milk are procured from seven dairy farms. One-half of the milk sampled from each farm is
Identify the following as either matched pair or independent samples. Also identify the experimental units, treatments, and response in each case.(a) Twelve persons are given a high-potency vitamin C capsule once a day. Another twelve do not take extra vitamin C. Investigators record the number of
A study is to be made of the relative effectiveness of two kinds of cough medicines in increasing sleep. Six people with colds are given medicine A the first night and medicine B the second night. Their hours of sleep each night are recorded.(a) Establish a 95% confidence interval for the mean
In an experiment conducted to see if electrical pricing policies can affect consumer behavior, 10 homeowners in Wisconsin had to pay a premium for power use during the peak hours. They were offered lower off-peak rates. For each home, the July on-peak usage (kilowatt hours) under the pricing
Laser guns for detecting speeders require an accurate measurement of distance. In one daily calibration test, police measure the known distances 164 feet and 104 feet. The difference in readings should be 60 but there is some variation. The differences (courtesy of Madison Police Department) for
A study about the effects of marijuana use concludes that persons who became persistent users before they reached the age of 18, and who remained persistent users until age 38, will lose several IQ points over that time span.5 The summary data, for the change in IQ from before marijuana use to age
Refer to the measurement of job satisfaction in Example 4. Rather than average score, researchers often prefer the proportion who respond "very satisfied." Using the data in Exercise 10.12, compare the proportion for clergy, p1, with the proportion for office supervisors, p2. (a) Find a 95%
Refer to the measurement of job satisfaction in Exercise 10.45. Using the data in Exercise 10.12, compare the proportion for firefighters, p1, with the proportion for office supervisors, p2.(a) Find a 95% confidence interval for the difference of proportions p1 - p2.(b) Perform the Z test for the
In a study of the relationship between temperament and personality, 49 female high school students who had a high level of reactivity (HRL) and 54 students who had a low level of reactivity (LRL) were classified according to their attitude to group pressure with the following results.Is resistance
Refer to Exercise 10.17 concerning a study on the relationship between child abuse and later criminal behavior. Suppose that from follow-ups of 85 boys who were abused in their preschool years and 120 boys who were not abused, it was found that 21 boys in the abused group and 11 boys in the non
The popular disinfectant Listerine is named after Joseph Lister, a British physician who pioneered the use of antiseptics. Lister conjectured that human infections might have an organic origin and thus could be prevented by using a disinfectant. Over a period of several years, he performed 75
According to the assumptions underlying the two independent samples design, (a) Are two observations from the same sample, say X2 and X4, (i) Independent? (ii) Do they always have the same distribution? (b) Are two observations from different samples, say X2 and Y2, (i) Independent? (ii) Do they
Referring to the data of Exercise 10.49, calculate a 95% confidence interval for the difference between the survival rates for the two groups.In Exercise 10.49
Random samples of 250 persons in the 30- to 40-year age group and 250 persons in the 60- to 70-year age group are asked about the average number of hours they sleep per night, and the following summary data are recorded.Do these data demonstrate that the proportion of persons who have
Referring to Exercise 10.51, denote by p1 and p2 the population proportions in the two groups who have In Exercise 10.51Random samples of 250 persons in the 30- to 40-year age group and 250 persons in the 60- to 70-year age group are asked about the average number of hours they sleep per night, and
A medical researcher conjectures that smoking can result in wrinkled skin around the eyes. By observing 150 smokers and 250 nonsmokers, the researcher finds that 95 of the smokers and 103 of the nonsmokers have prominent wrinkles around their eyes. (a) Do these data substantiate the belief that
In the survey on which Table D.12 of the Data Bank is based, a larger number of persons was asked to respond to the statement "I would characterize my political beliefs as liberal" on a seven point Likert scale from strongly disagree (1) to strongly agree (7). A count of those who strongly
A major clinical trial of a new vaccine for type-B hepatitis was conducted with a high-risk group of 1083 male volunteers. From this group, 549 men were given the vaccine and the other 534 a placebo. A follow-up of all these individuals yielded the data:(a) Do these observations testify that the
Records of drivers with a major medical condition (diabetes, heart condition, or epilepsy) and also a group of drivers with no known health conditions were retrieved from a motor vehicle department. Drivers in each group were classified according to their driving record in the last year.Let pD, pH,
Refer to Exercise 10.56. (a) Construct a 95% confidence interval for PE - PH- (b) Construct a 90% confidence interval for PH - PC- (c) Construct 95% confidence intervals for pD, pH, pE, and pC, individually.
Refer to Table D.12 of the Data Bank. The responses, of persons in the first and second age groups, on the frequency of credit card use question, have the summary statistics(a) Obtain a 98% confidence interval for the difference in the two population mean frequency of credit card use scores. (b)
Two versions of a new simplified tax form, Al and A2, need to be evaluated with respect to the time, in hours, it takes to complete the form. Forty persons were selected to fill out Form Al and 40 were selected to fill out Form A2. The summary statistics are:(a) Find a 95% confidence interval for
Refer to Table D.12 of the Data Bank. The responses, of persons in the first and third age groups to the average monthly amount charged, have the summary statisticsDetermine a 95% confidence interval for the difference of means.
Refer to the data in Exercise 10.60. Suppose you wish to establish that the mean response of 35-44 year olds is larger than that of 19-24 year olds by more than 150 dollars. (a) Formulate the null hypothesis and the alternative hypothesis. (b) State the test statistic and the rejection region with
A study of postoperative pain relief is conducted to determine if drug A has a significantly longer duration of pain relief than drug B. Observations of the hours of pain relief are recorded for 55 patients given drug A and 58 patients given drug B. The summary statistics are(a) Formulate H0 and
Consider the data of Exercise 10.62. (a) Construct a 90% confidence interval for μA - μB. (b) Give a 95% confidence interval for μA using the data of drug A alone.
Obtain s2pooled for the gaming data in the chapter opening.
Given the following two samples,obtain (a) s2pooled and (b) the value of the t statistic for testing H0: Î¼1 - Î¼2 = 2. State the d.f. of the t.
A fruit grower wishes to evaluate a new spray that is claimed to reduce the loss due to damage by insects. To this end, he performs an experiment with 27 trees in his orchard by treating 12 of those trees with the new spray and the other 15 trees with the standard spray. From the data of fruit
Referring to Exercise 10.66, construct an approximate t 95% confidence interval for the difference in mean yields between the new spray and the standard spray.
Refer to Exercise 10.59 but suppose, instead, that the sample sizes are 8 and 7 with the same summary statistics:(a) Test, with the approximate t procedure, that the population means are different. Use Î± = .05. (b) What assumptions did you make for your answer?
An investigation is conducted to determine if the mean age of welfare recipients differs between two cities A and B. Random samples of 75 and 100 welfare recipients are selected from city A and city B, respectively, and the following computations are made.(a) Do the data provide strong evidence
One semester, an instructor taught the same computer course at two universities located in different cities. He was able to give the same final at both locations. The student's scores provided the summary statistics.(a) Obtain a point estimate of Î¼1 - Î¼2.(b) Estimate the S.E.( - ).(c)
Refer to the data on the weight of wolves in Table D.9 of the Data Bank. A computer analysis produces the output(a) What is the conclusion to testing the equality of mean weights at level Î± = .05? (b) Test the null hypothesis that males weigh an average of 5 pounds more than females
Refer to the computer attitude scores (CAS) of students given in Table D.4 of the Data Bank. A computer analysis produces the output(a) What is the conclusion to testing the equality of mean computer attitude scores at level a = .05? (b) Find a 95% confidence interval for the mean attitude score
To compare the crop yields from two strains of wheat, A and B, an experiment was conducted at eight farms located in different parts of a state. At each farm, strain A was grown on one plot and strain B on another; all 16 plots were of equal sizes. Given below are data of yield in pounds per
Refer to the problem stated in Exercise 10.72, but now suppose that the study was conducted at 16 farms, of which 8 were selected for planting strain A and the other 8 for strain B. Here also the plots used were all of equal sizes. Recorded below are the data of yields in pounds per plot.(a) Is
In each of the following cases, how would you select the experimental units and conduct the experiment-matched pairs or independent samples? (a) Compare the mileage obtained from two gasolines. Twelve SUVs of various sizes are available. (b) Compare the drying times of two latex-based interior
A sample of river water is divided into two specimens. One is randomly selected to be sent to Lab A and the other is sent to Lab B. This is repeated for a total of nine times. The measurement of suspended solids at Lab B is subtracted from that of Lab A to obtain the differences(a) Is there strong
Two scales are available at a campus athletic facility. A student wonders if, on average, they give the same reading for weight. She and four others weigh themselves on both scales. The readings are(a) Find a 95% confidence interval for the mean difference in scale readings. (b) Based on your
An experiment is conducted to determine if the use of a special chemical additive with a standard fertilizer accelerates plant growth. Ten locations are included in the study. At each location, two plants growing in close proximity are treated. One is given the standard fertilizer, the other the
Referring to Exercise 10.77, suppose that the two plants at each location are situated in the east-west direction. In designing this experiment, you must decide which of the two plants at each location-the one in the east or the one in the west-is to be given the chemical additive. (a) Explain how,
Students can bike to a park on the other side of a lake by going around one side of the lake or the other. After much discussion about which was faster, they decided to perform an experiment. Among the 12 students available, 6 were randomly selected to follow Path A on one side of the lake and the
Rural and urban students are to be compared on the basis of their scores on a nationwide musical aptitude test. Two random samples of sizes 90 and 100 are selected from rural and urban seventh-grade students. The summary statistics from the test scores areConstruct a 98% confidence interval for the
Five pairs of tests are conducted to compare two methods of making rope. Each sample batch contains enough hemp to make two ropes. The tensile strength measurements are(a) Treat the data as 5 paired observations and calculate a 95% confidence interval for the mean difference in tensile strengths
An experiment was conducted to study whether cloud seeding reduces the occurrences of hail. At a hail-prone geographical area, seeding was done on 50 stormy days and another 165 stormy days were also observed without seeding. The following counts were obtained.Do these data substantiate the
Example 16, Chapter 8, presents the result that 158 male babies were born to 363 parents both of whom smoke? The same study found that 2685 male babies were born to 5045 parents, neither of which smoked. Obtain a 95% confidence interval of the increase in the proportion of male births when
A linguist wants to compare the writing styles in two magazines and one measure is the number of words per sentence. On the basis of 50 randomly selected sentences from each source, she findsDetermine a 98% confidence interval for the difference in mean number of word per sentences.
In the survey on which Table D.12 of the Data Bank is based, a large number of persons was each asked "Is it preferable to have 1% of your monthly charges donated to a charity of your choice rather than credited back to your account?" The full sample, larger than that in Table D.12, yielded the
We illustrate the MINITAB commands and output for the two-sample r test. The approximate t test is performed if you don't click Assume equal variances.Difference = mu (CI) - mu (C2) Estimate for difference: -3.17 95% CI for difference: (-7.61, 1.28) T-Test of difference = 0 (vs not =): T-Value =
Refer to the alligator data in Table D.11 of the Data Bank. Using the data on testosterone X4 from the Lake Apopka alligators, find a 95% confidence interval for the difference of means between males and females. There should be a large difference for healthy alligators. Comment on your conclusion.
Refer to the alligator data in Table D.11 of the Data Bank. Using the data on testosterone x4 for male alligators, compare the means for the two lake regions.(a) Should you pool the variances with these data?(b) Find a 90% confidence interval for the difference of means between the two lakes. Use
Refer to the bear data in Table D.6 of the Data Bank. Compare the head widths of males and females by obtaining a 95% confidence interval for the difference of means and also test equality versus a two-sided alternative with α = .05.
Refer to the marine growth of salmon data in Table D.7 of the Data Bank. Compare the mean growth of males and females by obtaining a 95% confidence interval for the difference of means and also test equality versus a two-sided alternative with α = .05.
Perform a test to determine if there is a significant difference between the population mean scores in Exercise 10.8. Use α = .05.
Refer to the physical fitness data in Table D.5 of the Data Bank. Find a 95% confidence interval for the mean difference of the pretest minus posttest number of situps. Also test that the mean difference is zero versus a two-sided alternative with α = .05.

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