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mathematics
statistics
Elementary Statistics 11th Edition Robert R. Johnson, Patricia J. Kuby - Solutions
Find the value of P for each of the hypothesis tests in Exercise 9.95; state the decision using a = 0.05 In Exercise 9.95 a. Ho: p = 0.70 Ha: p > 0.70 with the sample n = 300 and x = 224 b. Ho: p = 0.50 Ha: p < 0.50 with the sample n = 450 and x = 207 c. Ho: p = 0.35 vs Ha: p ≠0.35 with the
Determine the p-value for each of the following hypothesis-testing situations.
Determine the test criteria that would be used to test the following hypotheses when z is used as the test statistic and the classical approach is used
Determine the test criteria that would be used to test the following hypotheses when z is used as the test statistic and the classical approach is used.
The data that follow are from two random samples of 37 college males and 42 college females with respect to their commute times to e.a. What are the populations of interest? b. Describe statistically the distribution of both the male and the female €œcommute time€ data using
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
PC users are often victimized by hardware problems. A study revealed that hardware problems reported to manufacturers could not be fixed by one in three owners of personal computers. Home PC owners fared even worse than those with work PCs, facing longer waits for service and getting even fewer
Two randomly selected groups of citizens were exposed to different media campaigns that dealt with the image of a political candidate. One week later, the citizen groups were surveyed to see whether they would vote for the candidate.The results were as follows:Is there sufficient evidence to show a
In a survey of families in which both parents work, one of the questions asked was, “Have you refused a job, promotion, or transfer because it would mean less time with your family?” A total of 200 men and 200 women were asked this question.“Yes” was the response given by 29% of the men and
Consumer Reports conducted a survey of 1000 adults concerning wearing bicycle helmets. One of the questions presented to 25- to 54-year olds was whether they wear a helmet most of the time while biking or cycling. This was further broken down to whether or not they had a child at home. Eighty-seven
A Harris Interactive poll found that 50% of Democrats follow professional football while 59% of Republicans follow the sport. If the poll results were based on samples of 875 Democrats and 749 Republicans, determine, at the 0.05 level of significance, if the viewpoint of more Republicans following
The Committee of 200, a professional organization of preeminent women entrepreneurs and corporate leaders, reported the following: 60% of women MBA students say, “Businesses pay their executives too much money” and 50% of the men MBA students agreed. a. Does there appear to be a difference in
Both parents and students have many concerns when considering colleges. One of the top three concerns, based on a College Partnership study, is “Choosing best major/career.” Nineteen percent of the parents reported “Choosing best major/career” as a major concern whereas 15% of students
A 2005 Harris Interactive for Korbel poll found that 63% of men and 55% of women think that it is okay for women to make marriage proposals to men. An 8% difference may or may not be statistically significant.What size sample is required to make this difference significant? a. If the preceding
Adverse side effects are always a concern when testing and trying new medicines. Placebo-controlled clinical studies were conducted in patients 12 years of age and older who were receiving €œonce-a-day€ doses of Allegra, a seasonal allergy dru g. The following results were
Forty-one small lots of experimental product were manufactured and tested for the occurrence of a particular indication that is an attribute in nature yet causes rejection of the part. Thirty-one lots were made using one particular processing method, and ten lots were made using a second processing
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 data
a. Verify that B(100, 0.3) and B(100, 0.4) satisfy all guidelines.b. Use a computer to randomly generate 200 samples from each of the binomial populations. Find the observed proportion for each sample and the value of the 200 differences between two proportions.c. Describe the observed sampling
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test the following claims: a. The variances of populations A and B are not equal. b. The standard deviation of population I is larger than the standard deviation of population II. c. The ratio of the
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test the following claims: a. The standard deviation of population X is smaller than the standard deviation of population Y. b. The ratio of the variances of population A over population B is greater than 1.
Express the Ho and Ha of Example 10. 17 equivalently in terms of standard deviations
Using the F(df1, df2, a) notation, name each of the critical values shown on the following figures.
Find the following critical values for F from Tables 9A, 9B, and 9C in Appendix B. a. F(24, 12, 0.05) e. F(15, 18, 0.025) b. F(30, 40, 0.01) f. F(15, 9, 0.025) c. F(12, 10, 0.05) g. F(40, 30, 0.05) d. F(5, 20, 0.01) h. F(8, 40, 0.01)
Determine the p-value that would be used to test the following hypotheses when F is used as the test statistic:
With all the media attention from the Dancing With the Stars program, local dance studios are seeing an upswing in the numbers of people interested in taking ballroom dancing lessons.Two samples of 15 students are to be judged before taking any lessons and then again after five lessons. The
Determine the critical region and critical value(s) that would be used to test the following hypotheses using the classical approach when F_ is used as the test statisti
Calculate F given s1 = 3.2 and s2 = 2.6
Calculate F given s1 2 = 3.2 and s2 2 = 2.6.
What would be the value of F_ in Example 10. 19 If were used? Why is it less than 1?
Do the lengths of boys€™ names have more variation than the lengths of girls€™ names? With current names like €œNathaniel€ and €œChristopher€ versus €œIan€ and €œJack,€ it certainly appears that
Two independent random samples of size 25 were taken from an English class and a chemistry class at a local community e. Students in both classes were asked to draw a 3-inch line to the best of their ability without any measuring device (ruler, etc.).The following data resulted:At the 0.05 level of
A study in Pediatric Emergency Care compared the injury severity between younger and older children. One measure reported was the Injury Severity Score (ISS). The standard deviation of ISS’s for 37 children 8 years or younger was 23.9, and the standard deviation for 36 children older than 8 years
A bakery is considering buying one of two gas ovens. The bakery requires that the temperature remain constant during a baking operation. A study was conducted to measure the variance in temperature of the ovens during the baking process. The variance in temperature before the thermostat restarted
Given this set of paired data:Find: a. The paired differences, d = A = B for this set of data b. The mean of the paired differences c. The standard deviation sd of the paired differences
Referring to Applied Example 10. 20c. Use a computer or calculator to calculate the p-value for F(237, 305) = 1.36
The quality of an end product is somewhat determined by the quality of the materials useCalculate the observed value of F, F, for comparing the variances of these two sets of dat a.
Several counties in Minnesota and Wisconsin were randomly selected and information about the 2007 sweet corn crop was collected. The following yield rates in tons of sweet corn per acre harvested resulted.a. Is there a difference in the variability of county yields as measured by the standard
Professional athletes€™ salaries are often criticized for being €œover the top.€ Many also earn even more money through endorsements. Various NBA (National Basketball Association) and MLB (Major League Baseball) players can be seen in many high-profile endorsements.
The data that follow are from two random samples of 37 college males and 42 college females with respect to their commute times to e.a. Do the distributions of €œcommute time€ for males and females appear to be similar in distribution? Center? Spread? Discuss your responses.
A constant objective in the manufacture of contact lenses is improving the level and variation for those features that affect lens power and visual acuity. One such feature involves the tooling from which lenses are ultimately manufacture d. The results of two initial process development runs were
Americans snooze more on the weekends, according to a poll of 1506 adults for the National Sleep Foundation and reported in a USA Today Snapshot during April 2005.Two independent random samples were taken at a large industrial complex. The workers selected in one sample were asked, €œHow
What dollar amount should someone spend on a Valentine€™s Day gift for you? The results found by a Greenfield Online survey of 653 respondents are pictured in the accompanying graphic. Random samples were selected in central New York State with the following results.a. Construct a
a. Two independent samples, each of size 3, are drawn from a normally distributed population. Find the probability that one of the sample variances is at least 19 times larger than the other one. b. Two independent samples, each of size 6, are drawn from a normally distributed population. Find the
Use a computer to demonstrate the truth of the theory presented in this section. a. The underlying assumptions are “the populations are normally distributed,” and while conducting a hypothesis test for the equality of two standard deviations, it is assumed that the standard deviations are
Find t(15, 0.025). Describe the role this number plays when forming a confidence interval for the mean difference.
It was stated in this section that the F-test is very sensitive to minor departures from the assumptions. Repeat Exercise 10. 139 using N(100, 20) and N(120, 30). Notice that the only change from Exercise 10. 139 is the seemingly slight increase in the standard deviation of the second population.
Using a 95% confidence interval, estimate the mean difference in IQ between the oldest and the youngest members (brothers and sisters) of a family based on the following random sample of IQs.Assume normality.
The diastolic blood pressure readings for 15 patients were determined using two techniques: the standard method used by medical personnel and a method using an electronic device with a digital readout. The results were as follows:Assuming blood pressure is normally distributed, determine the 90%
We want to know which of two types of filters should be used. A test was designed in which the strength of a signal could be varied from zero to the point where the operator first detects the image. At that point, the intensity setting is recorded. Lower settings are better. Twenty operators were
At the end of their first day at training camp, 10 new recruits participated in a rifle-shooting competition. The same 10 competed again at the end of a full week of training and practice. Their resulting scores are shown in the following table.Does this set of 10 pairs of data show that there was
Salt-free diets are often prescribed to people with high blood pressure.The following data were obtained from an experiment designed to estimate the reduction in diastolic blood pressure as a result of following a salt-free diet for two weeks. Assume diastolic readings are normally distributed.a.
Immediate-release medications quickly deliver their drug content, with the maximum concentration reached in a short time; sustained-release medications, on the other hand, take longer to reach maximum concentration. As part of a study, immediaterelease codeine (irc) was compared with
A test that measures math anxiety was given to 50 male and 50 female students. The results were as follows:Construct a 95% confidence interval for the difference between the mean anxiety scores.
a. Find the 95% confidence interval for m d 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 Example10. 4.
The same achievement test is given to soldiers selected at random from two units. The scores they attained are summarized as follows:Construct a 90% confidence interval for the difference in the mean level of the two units.
Experimentation with a new rocket nozzle has led to two slightly different designs. The following data summaries resulted from testing these two designs.Determine the 99% confidence interval for the difference in the means for these two rocket nozzles.
An achievement test in a beginning computer science course was administered to two groups. One group had had a previous computer science course in high school; the other group had not. The test results follow. Assuming test scores are normal, construct a 98% confidence interval for the difference
Two methods were used to study the latent heat of ice fusion. Both method A (an electrical method) and method B (a method of mixtures) were conducted with the specimens cooled to _0.72_C The data in the following table represent the change in total heat from 0.72°C to water at 0°C in
Sucrose, ordinary table sugar, is probably the single most abundant pure organic chemical in the world and the one most widely known to non-chemists. Whether from sugar cane (20% by weight) or sugar beets (15% by weight), and whether raw or refined, common sugar is still sucrose. Fifteen U.S. sugar
George Johnson is the head coach of a college football team that trains and competes at home on artificial turf. George is concerned that the 40-yard sprint time recorded by his players and others increases substantially when running on natural turf as opposed to artificial turf. If so, there is
A test concerning some of the fundamental facts about acquired immunodeficiency syndrome (AIDS) was administered to two groups, one consisting of college graduates and the other consisting of high school graduates. A summary of the test results follows:Do these data show that the college graduates,
Some 20 million Americans visit chiropractors annually, and the number of practitioners in the United States is 55,000, nearly double the number two decades ago, according to the American Chiropractic Association. The New England Journal of Medicine released a report showing the results of a study
To compare the merits of two short-range rockets, 8 of the first kind and 10 of the second kind are fired at a target. If the first kind has a mean target error of 36 feet and a standard deviation of 15 feet and the second kind has a mean target error of 52 feet and a standard deviation of 18 feet,
The material used in making parts affects not only how long the part lasts but also how difficult it is to repair. The following measurements are for screw torque removal for a specific screw after several operations of use. The first row lists the part number, the second row lists the screw torque
All students who enroll in a certain memory course are given a pre-test before the course begins. At the completion of the course, 10 students are selected at random and given a post-test; their scores are listed here.MINITAB was used to find the 95% confidence interval for the mean improvement in
A group of 17 students participated in an evaluation of a special training session that claimed to improve memory. The students were randomly assigned to two groups: group A, the test group, and group B, the control group. All 17 students were tested for their ability to remember certain material.
At a large university, a mathematics placement exam is administered to all students. This exam has a history of producing scores with a mean of 77. Samples of 36 male students and 30 female students are randomly selected from this year€™s student body and the following scores recorded.a.
A survey was conducted to determine the proportion of Democrats as well as Republicans who support a “get tough” policy in South America. The results of the survey were as follows: Democrats: n = 250 number in support = 120 Republicans: n = 200 number in support = 105. Construct the 98%
A consumer group compared the reliability of two comparable microcomputers from two different manufacturers. The proportion requiring service within the first year after purchase was determined for samples from each of two manufacturers.Find a 0.95 confidence interval for p1 - p2
“It’s a draw,” according to two Australian researchers. “By age 25, up to 29% of all men and up to 34% of all women have some gray hair, but this difference is so small that it’s considered insignificant” (“Silver Threads Among the Gold: Who’ll Find Them First, a Man or a Woman?”
According to “Venus vs. Mars” in the May/June 2005 issue of Arthritis Today, men and women may be more alike than we think. The Boomers Wellness Lifestyle Survey of men and women aged 35 to 65 found that 88% of women considered “managing stress” important for maintaining overall
A study in the New England Journal of Medicine reported that based on 987 deaths in southern California, right-handers died at an average age of 75 and left-handers died at an average age of 66. In addition, it was found that 7.9% of the lefties died from accident-related injuries, excluding
Who wins disputed cases whenever there is a change made to the tax laws, the taxpayer or the Internal Revenue Service (IRS)? The latest trend indicates that the burden of proof in all court cases has shifted from taxpayers to the IRS, which tax experts predict could set off more intrusive
In determining the “goodness” of a test question, a teacher will often compare the percentage of better students who answer it correctly with the percentage of poorer students who answer it correctly. One expects that the proportion of better students who will answer the question correctly is
A manufacturer designed an experiment to compare the differences between men and women with respect to the times they require to assemble a product. A total of 15 men and 15 women were tested to determine the time they required, on average, to assemble the product. The time required by the men had
Ten subjects with borderline-high cholesterol levels were randomly recruited for a study that involved taking a nutrition education class. Cholesterol readings were taken before the class and 3 months after the class.Let d = preclass cholesterol - postclass cholesterol. Excel was used to find the
A soft drink distributor is considering two new models of dispensing machines. Both the Harvard Company machine and the Fizzit machine can be adjusted to fill the cups to a certain mean amount.However, the variation in the amount dispensed from cup to cup is a primary concern. Ten cups dispensed
Mindy Fernandez is in charge of production at the new sport-utility vehicle (SUV) assembly plant that just opened in her town. Lately she has been concerned that the wheel lug studs do not match the chrome lug nuts close enough to keep the assembly of the wheels operating smoothly.Workers are
Do students who register for early morning classes typically do better than those who sign up for later day classes? Random samples from two elementary statistics classes were taken to determine if a significant difference exists in the variability and means of grades for a probability test given
A research project was undertaken to evaluate the amount of force needed to elicit a designated response on equipment made from two distinct designs: the existing design and an improved design. The expectation was that new design equipment would require less force than the current equipment. Fifty
Use a computer or calculator to find the 95% confidence interval for estimating m d based on these paired data and assuming normality:
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. The gains (in
a. Describe a sampling plan you might use to select two independent samples of male and female commute times to e. b. Describe a sampling plan you might use to select two dependent samples of male and female commute times to e. c. Do you foresee any advantages for using one plan over the other?
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 weeks, A will
An unmarried 19-year-old who has just purchased his/her own 2-year-old Honda Civic might be asking,“Why does auto insurance cost so much?”There are many reasons, according to the insurance agent, one of which is whether the driver is male or female. The insurance rates listed below are for a
In evaluating different measuring instruments, one must first determine whether there is a systematic difference between the instruments. Lenses with several different powers were measured once each by two different instruments. The measurement differences (Instrument A €“ Instrument B)
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 post-test and pre-test scores. b. Following a special training session, it is believed that the mean of the difference in performance
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 post-test and the pre-test scores is greater than 15. b. The mean weight gain, after the change in diet for the laboratory animals, is at least 10
Determine the p-value for each hypothesis test for the mean difference.
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 Bloomberg News poll found that Americans plan to keep spending down over the next six months due to the uncertain economy (USA Today, September 17, 2009). Suppose a group of 15 households noted their household spending in March and then noted their household spending six months later in
A random sample of 10 speed skaters, all of the relatively same experience and speed, were selected to try out a new specialty blade.The difference in the short track times were measured as current blade time – specialty blade time, resulting in mean difference of 0.165 second with a standard
The corrosive effects of various soils on coated and uncoated steel pipe were tested by using a dependent sampling plan. The data collected are summarized by n = 40 _d ∑ 220and ∑d2 = 6222 where d is the amount of corrosion on the coated portion subtracted from the amount of corrosion on the
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 their comprehension of the information on a scale from 1 to 10, where 10 was complete comprehension.The same 26 participants were
Complete the hypothesis test with alternative Hypothesis m d > 0 based on the paired data that follow and d = B €“ A Use a = 0.05 Assume normality.a. Solve using the p-value approach. b. Solve using the classical approach.
Complete the hypothesis test with alternative Hypothesis m d ‰ 0 based on the paired data that follow and d = O €“ Y Use a = 0.01 Assume normalitya. Solve using the p-value approach. b. Solve using the classical approach.
Use a computer or calculator to complete the hypothesis test with alternative hypothesis m d
Ten randomly selected college students who participated in a learning community were given pre€“self-esteem and post€“self-esteem 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
In reference to the college students who participated in a learning community in Exercise 10. 36, 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 pre€“self-esteem and
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
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