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Introduction To Probability And Statistics 14th Edition William Mendenhall, Robert Beaver, Barbara Beaver - Solutions

A drug manufacturer claimed that the mean potency of one of its antibiotics was 80%. A random sample of n = 100 capsules were tested and produced a sample mean of = 79.7% with a standard deviation of s = .8%. Do the data present sufficient evidence to refute the manufacturer's claim? Let α =
A company was contemplating the installation of a flextime schedule in which a worker schedules his or her work hours or compresses work weeks. The company estimates that it needs a minimum mean of 7 hours per day per assembly worker in order to operate effectively. Each of a random sample of 80 of
An article in Time describing various aspects of American life indicated that higher educational achievement paid off! College grads work 7.4 hours per day, fewer than those with less than a college education. Suppose that the average work day for a random sample of n = 100 individuals who had less
What is normal, when it comes to people's body temperatures? A random sample of 130 human body temperatures, provided by Allen Shoemaker3 in the Journal of Statistical Education, had a mean of 98.25° and a standard deviation of 0.73°. Does the data indicate that the average body temperature for
Some sports that involve a significant amount of running, jumping, or hopping put participants at risk for Achilles tendinopathy (AT), an inflammation and thickening of the Achilles tendon. A study in The American Journal of Sports Medicine looked at the diameter (in mm) of the affected tendons for
Independent random samples of 80 measurements were drawn from two quantitative populations, 1 and 2. Here is a summary of the sample data:a. If your research objective is to show that µ1 is larger than µ2, state the alternative and the null hypotheses that you would choose for a
Independent random samples of 36 and 45 observations are drawn from two quantitative populations, 1 and 2, respectively. The sample data summary is shown here:Do the data present sufficient evidence to indicate that the mean for population 1 is smaller than the mean for population 2? Use one of the
Refer to Exercise 9.1. Suppose that the observed value of the test statistic was z = 2.16. For the rejection regions constructed in parts a and b of Exercise 9.1, draw the appropriate conclusion for the tests. If appropriate, give a measure of the reliability of your conclusion. Exercise 9.1 Find
Suppose you wish to detect a difference between μ1 and μ2 (either μ1 > μ2 or μ1 < μ2) and, instead of running a two-tailed test using α = .05, you use the following test procedure. You wait until you have collected the sample data and have calculated 1 and 2. If 1 is larger than 2,
An experiment was planned to compare the mean time (in days) required to recover from a common cold for persons given a daily dose of 4 milligrams (mg) of vitamin C versus those who were not given a vitamin supplement. Suppose that 35 adults were randomly selected for each treatment category and
As Americans become more conscious about the importance of good nutrition, researchers theorize that the consumption of red meat may have decreased over the last 10 years. A researcher selects hospital nutrition records for 400 subjects surveyed 10 years ago and compares the average amount of beef
Analyses of drinking water samples for 100 homes in each of two different sections of a city gave the following means and standard deviations of lead levels (in parts per million):a. Calculate the test statistic and its p-value to test for a difference in the two population means. Use the p-value
As a group, students majoring in the engineering disciplines have the highest salary expectations, followed by those studying the computer science fields, according to results of NACE's 2010 Student Survey. To compare the starting salaries of college graduates majoring in engineering and computer
In Exercise 8.20, we explored the average cost of lodging at three different hotel chains. We randomly select 50 billing statements from the computer databases of the Marriott, Westin, and Doubletree hotel chains, and record the nightly room rates. A portion of the sample data is shown in the
Refer to Exercise 9.25. The table below shows the sample data collected to compare the average room rates at the Westin and Doubletree hotel chains.a. Do the data provide sufficient evidence to indicate a difference in the average room rates for the Westin and the Doubletree hotel chains? Use
Looking for a great airfare? Consumer Reports has several hints about how to minimize your costs, which include being flexible about travel dates and times, checking multiple websites, and knowing when to book your flight. One suggestion involved checking fares at "secondary" airports-airports that
In Exercise 8.52, you compared the effect of stress in the form of noise on the ability to perform a simple task. Seventy subjects were divided into two groups; the first group of 30 subjects acted as a control, while the second group of 40 was the experimental group. Although each subject
Of the 130 people in Exercise 9.16, 65 were female and 65 were male. The means and standard deviations of their temperatures are shown below.a. Use the p-value approach to test for a significant difference in the average temperatures for males versus females. b. Are the results significant at the
Find the appropriate rejection regions for the large-sample test statistic z in these cases: a. A left-tailed test at the 1% significance level. b. A two-tailed test with α = .01. c. Suppose that the observed value of the test statistic was z = - 2.41. For the rejection regions constructed in
A random sample of n = 1000 observations from a binomial population produced x = 279. a. If your research hypothesis is that p is less than .3, what should you choose for your alternative hypothesis? Your null hypothesis? b. What is the critical value that determines the rejection region for your
A random sample of n = 1400 observations from a binomial population produced x = 529. a. If your research hypothesis is that p differs from .4, what hypotheses should you test? b. Calculate the test statistic and its p-value. Use the p-value to evaluate the statistical significance of the results
A random sample of 120 observations was selected from a binomial population, and 72 successes were observed. Do the data provide sufficient evidence to indicate that p is greater than .5? Use one of the two methods of testing presented in this section, and explain your conclusions.
According to a survey in PARADE magazine, almost half of parents say their children's weight is fine. Only 9% of parents describe their children as overweight. However, the American Obesity Association says the number of overweight children and teens is at least 15%. Suppose that you sample n = 750
A peony plant with red petals was crossed with another plant having streaky petals. A geneticist states that 75% of the offspring resulting from this cross will have red flowers. To test this claim, 100 seeds from this cross were collected and germinated, and 58 plants had red petals. a. What
Of those women who are diagnosed to have early-stage breast cancer, one-third eventually die of the disease. Suppose a community public health department instituted a screening program to provide for the early detection of breast cancer and to increase the survival rate p of those diagnosed to have
Suppose that 10% of the fields in a given agricultural area are infested with the sweet potato whitefly. One hundred fields in this area are randomly selected, and 25 are found to be infested with whitefly. a. Assuming that the experiment satisfies the conditions of the binomial experiment, do the
In a head-to-head taste test of store-brand foods versus national brands, Consumer Reports found that it was hard to find a taste difference in the two. If the national brand is indeed better than the store brand, it should be judged as better more than 50% of the time. a. State the null and
In Exercise 9.37, we tried to prove that the national brand tasted better than the store brand. Perhaps, however, the store brand has a better taste than the national brand! If this is true, then the store brand should be judged as better more than 50% of the time. a. State the null and alternative
An experimenter has prepared a drug-dose level that he claims will induce sleep for at least 80% of people suffering from insomnia. After examining the dosage we feel that his claims regarding the effectiveness of his dosage are inflated. In an attempt to disprove his claim, we administer his
Find the p-value for the following large-sample z tests:a. A right-tailed test with observed z = 1.15b. A two-tailed test with observed z = - 2.78c. A left-tailed test with observed z = - 1.81
According to a new nationwide survey from the Pew Research Center's Social & Demographic Trends project, 62% of Americans consider a landline phone a necessity of life, down from 68% last year, and only 43% of Americans consider a TV a necessity. Both questions were on the second of two forms used
The Humane Society reports that there are approximately 77.5 million dogs owned in the United States and that approximately 40% of all U.S. households own at least one dog. In a random sample of 300 households, 114 households said that they owned at least one dog. Does this data provide sufficient
Independent random samples of n1 = 140 and n2 = 140 observations were randomly selected from binomial populations 1 and 2, respectively. Sample 1 had 74 successes, and sample 2 had 81 successes.a. Suppose you have no preconceived idea as to which parameter, p1 or p2, is the larger, but you want
Refer to Exercise 9.42. Suppose, for practical reasons, you know that p1 cannot be larger than p2. a. Given this knowledge, what should you choose as the alternative hypothesis for your statistical test? The null hypothesis? b. Does your alternative hypothesis in part a imply a one- or two-tailed
Independent random samples of 280 and 350 observations were selected from binomial populations 1 and 2, respectively. Sample 1 had 132 successes, and sample 2 had 178 successes. Do the data present sufficient evidence to indicate that the proportion of successes in population 1 is smaller than the
An experiment was conducted to test the effect of a new drug on a viral infection. After the infection was induced in 100 mice, the mice were randomly split into two groups of 50. The first group, the control group, received no treatment for the infection, and the second group received the drug.
A new study (Exercise 7.12) indicates that tai chi, an ancient Chinese practice of exercise and meditation, may relieve symptoms of chronic painful fibromyalgia. The study assigned 66 fibromyalgia patients to take either a 12- week tai chi class (n1 = 33), or attend a wellness education class (n2 =
In Exercise 8.57, you investigated whether Mars, Inc., uses the same proportion of red M&M'S in its plain and peanut varieties. Random samples of plain and peanut M&M'S provide the following sample data for the experiment:Use a test of hypothesis to determine whether there is a significant
A 4-year experiment involving 4532 women, reported in The Press Enterprise, was conducted at 39 medical centers to study the benefits and risks of hormone replacement therapy (HRT). Half of the women took placebos and half took Prempro, a widely prescribed type of hormone replacement therapy. There
Refer to Exercise 9.48. Calculate a 99% lower one-sided confidence bound for the difference in the risk of dementia for women using hormone replacement therapy versus those who do not. Would this difference be of practical importance to a woman considering HRT? Explain. Exercise 9.48 A 4-year
For the three tests given in Exercise 9.4, use the p-value to determine the significance of the results. Explain what "statistically significant" means in terms of rejecting or accepting H0 and Ha.
A large study was conducted to test the effectiveness of clopidogrel in combination with aspirin in warding off heart attacks and strokes. The trial involved more than 15,500 people 45 years of age or older from 32 countries, including the United States, who had been diagnosed with cardiovascular
Does a baby's sleeping position affect the development of motor skills? In one study, published in the Archives of Pediatric Adolescent Medicine, 343 full-term infants were examined at their 4-month checkups for various developmental milestones, such as rolling over, grasping a rattle, reaching for
a. Define α and β for a statistical test of hypothesis. b. For a fixed sample size n, if the value of α is decreased, what is the effect on β? c. In order to decrease both α and β for a particular alternative value of µ, how must the sample size change?
What conditions must be met so that the z test can be used to test a hypothesis concerning a population mean µ?
Refer to Exercise 8.33 and the collection of water samples to estimate the mean acidity (in pH) of rainfalls. As noted, the pH for pure rain falling through clean air is approximately 5.7. The sample of n = 40 rainfalls produced pH readings with = 3.7 and s = .5. Do the data provide sufficient
A manufacturer of automatic washers provides a particular model in one of three colors. Of the first 1000 washers sold, it is noted that 400 were of the first color. Can you conclude that more than one-third of all customers have a preference for the first color? a. Find the p-value for the
Born between 1980 and 1990, Generation Next was the topic of Exercise 8.64. In a survey of 500 female and 500 male students in Generation Next, 345 of the females and 365 of the males reported that they decided to attend college in order to make more money. a. Is there a significant difference in
The pH factor is a measure of the acidity or alkalinity of water. A reading of 7.0 is neutral; values in excess of 7.0 indicate alkalinity; those below 7.0 imply acidity. Loren Hill states that the best chance of catching bass occurs when the pH of the water is in the range 7.5 to 7.9. Suppose you
A random sample of n = 35 observations from a quantitative population produced a mean = 2.4 and a standard deviation s = .29. Suppose your research objective is to show that the population mean m exceeds 2.3. a. Give the null and alternative hypotheses for the test. b. Locate the rejection region
In Exercise 8.34, an Advertising Age white paper reported the number of minutes spent doing household chores for women when compared to men. However, there may be a difference among men, depending on the generation to which they belong. The information that follows is adapted from these data and is
In an article entitled "A Strategy for Big Bucks," Charles Dickey discusses studies of the habits of white-tailed deer that indicate that they live and feed within very limited ranges-approximately 150 to 205 acres. To determine whether there was a difference between the ranges of deer located in
In a study to assess various effects of using a female model in automobile advertising, 100 men were shown photographs of two automobiles matched for price, color, and size, but of different makes. One of the automobiles was shown with a female model to 50 of the men (group A), and both automobiles
Random samples of 200 bolts manufactured by a type A machine and 200 bolts manufactured by a type B machine showed 16 and 8 defective bolts, respectively. Do these data present sufficient evidence to suggest a difference in the performance of the machine types? Use α = .05.
Exercise 7.65 reported that the biomass for tropical woodlands, thought to be about 35 kilograms per square meter (kg/m2), may in fact be too high and that tropical biomass values vary regionally-from about 5 to 55 kg/m2. Suppose you measure the tropical biomass in 400 randomly selected
In a study to compare ethnic differences in adolescents' social stress, researchers recruited subjects from three middle schools in Houston, Texas. A tabulation of student responses to a question regarding their socioeconomic status (SES) compared with other families in which the students chose one
Refer to Exercise 9.65. Some thought should have been given to designing a test for which Î² is tolerably low when p1 exceeds p2 by an important amount. For example, find a common sample size n for a test with Î± = .05 and Î² ‰¤ .20 when in fact p1 exceeds p2 by 0.1.Exercise 9.65In a study
In a comparison of the mean 1-month weight losses for women aged 20-30 years, these sample data were obtained for each of two diets:Do the data provide sufficient evidence to indicate that diet I produces a greater mean weight loss than diet II? Use Î± = .05.
A test of the breaking strengths of two different types of cables was conducted using samples of n1 = n2 = 100 pieces of each type of cable.Do the data provide sufficient evidence to indicate a difference between the mean breaking strengths of the two cables? Use Î± = .05.
Refer to Exercise 9.6. a. Calculate the p-value for the test statistic in part d. b. Use the p-value to draw a conclusion at the 5% significance level. c. Compare the conclusion in part b with the conclusion reached in part d of Exercise 9.6. Are they the same? Exercise 9.6 A random sample of n =
The braking ability was compared for two 2012 automobile models. Random samples of 64 automobiles were tested for each type. The recorded measurement was the distance (in feet) required to stop when the brakes were applied at 50 miles per hour. These are the computed sample means and variances:Do
A fruit grower wants to test a new spray that a manufacturer claims will reduce the loss due to insect damage. To test the claim, the grower sprays 200 trees with the new spray and 200 other trees with the standard spray. The following data were recorded:a. Do the data provide sufficient evidence
A biologist hypothesizes that high concentrations of actinomycin D inhibit RNA synthesis in cells and hence the production of proteins as well. An experiment conducted to test this theory compared the RNA synthesis in cells treated with two concentrations of actinomycin D: .6 and .7 microgram per
How do California high school students compare to students nationwide in their college readiness, as measured by their SAT scores? The national average scores for the class of 2010 were 501 on the critical reading portion, 516 on the math portion, and 492 on the writing portion. Suppose that 100
In a maze running study, a rat is run in a T maze and the result of each run recorded. A reward in the form of food is always placed at the right exit. If learning is taking place, the rat will choose the right exit more often than the left. If no learning is taking place, the rat should randomly
Polychlorinated biphenyls (PCBs) have been found to be dangerously high in some game birds found along the marshlands of the southeastern coast of the United States. The Federal Drug Administration (FDA) considers a concentration of PCBs higher than 5 parts per million (ppm) in these game birds to
Refer to Exercise 9.75.a. Calculate β and 1 - β if the true mean ppm of PCBs is 6 ppm.b. Calculate b and 1 - β if the true mean ppm of PCBs is 7 ppm.c. Find the power, 1 - β, when µ = 8, 9, 10, and 12. Use these values to construct a power curve for the test in Exercise 9.75.d. For what values
If you choose to marry, what type of wedding site will you pick? A USA Today snapshot claims that 43% of all brides-to-be choose a house of worship for their wedding site.In a follow-up study, a random sample of 100 brides-to-be found that 46 of those sampled had chosen or would choose a house of
It is a well-accepted fact that males are taller on the average than females. But how much taller? The genders of 105 biomedical students (Exercise 1.54) were also recorded and the data are summarized below:a. Perform a test of hypothesis to either confirm or refute our initial claim that males are
The state of California monitors the progress of elementary-aged students whose native language is not English using the California English Language Development Test. The test results for two school districts in Riverside County for the 2009-2010 school year follow. The proportion given is the
Refer to Exercise 9.6. You want to test H0: µ = 2.3 against Ha: µ > 2.3.a. Find the critical value of used for rejecting H0.b. Calculate β = P(accept H0 when µ = 2.4).c. Repeat the calculation of b for µ = 2.3, 2.5, and 2.6.d. Use the values of β from parts b and c to graph the power
How much training time does it take to become a world-class breaststroke swimmer? A survey published in The American Journal of Sports Medicine reported the number of meters per week swum by two groups of swimmers-those who competed only in breaststroke and those who competed in the individual
Refer to Exercise 9.80.a. Construct a 99% confidence interval for the difference in the average number of meters swum by breaststroke versus individual medley swimmers.b. How much longer do pure breaststroke swimmers practice that stroke than individual medley swimmers? What is the practical reason
A random sample of 100 observations from a quantitative population produced a sample mean of 26.8 and a sample standard deviation of 6.5. Use the p-value approach to determine whether the population mean is different from 28. Explain your conclusions.
On Wednesday, January 27, 1988, the front page of the New York Times read, "Heart attack risk found to be cut by taking aspirin: Lifesaving effects seen." A very large study of U.S. physicians showed that a single aspirin tablet taken every other day reduced by one-half the risk of heart attack in
Find the following t-values in Table 4 of Appendix I: a. t.05 for 5 df b. t.025 for 8 df c. t.10 for 18 df d. t.025 for 30 df
The number of passes completed by Ben Roethlisberger, quarterback for the Pittsburgh Steelers, was recorded for each of the 12 regular season games in which he played during the fall of 2010 (www.ESPN.com)a. A stem and leaf plot of the n = 12 observations is shown below: Stem-and-Leaf Display:
A dairy is in the market for a new container-filling machine and is considering two models, manufactured by company A and company B. Ruggedness, cost, and convenience are comparable in the two models, so the deciding factor is the variability of fills. The model that produces fills with the smaller
Refer to Exercise 10.100. Wishing to demonstrate that the variability of fills is less for her model than for her competitor's, a sales representative for company A acquired a sample of 30 fills from her company's model and a sample of 10 fills from her competitor's model. The sample variances were
A chemical manufacturer claims that the purity of his product never varies by more than 2%. Five batches were tested and given purity readings of 98.2, 97.1, 98.9, 97.7, and 97.9%. a. Do the data provide sufficient evidence to contradict the manufacturer's claim? b. Find a 90% confidence interval
A cannery prints "weight 16 ounces" on its label. The quality control supervisor selects nine cans at random and weighs them. She finds = 15.7 and s = .5. Do the data present sufficient evidence to indicate that the mean weight is less than that claimed on the label?
A psychologist wishes to verify that a certain drug increases the reaction time to a given stimulus. The following reaction times (in tenths of a second) were recorded before and after injection of the drug for each of four subjects:Test at the 5% level of significance to determine whether the drug
At a time when energy conservation is so important, some scientists think closer scrutiny should be given to the cost (in energy) of producing various forms of food. Suppose you wish to compare the mean amount of oil required to produce 1 acre of corn versus 1 acre of cauliflower. The readings (in
The effect of alcohol consumption on the body appears to be much greater at high altitudes than at sea level. To test this theory, a scientist randomly selects 12 subjects and randomly divides them into two groups of six each. One group is put into a chamber that simulates conditions at an altitude
The closing prices of two common stocks were recorded for a period of 15 days. The means and variances area. Do these data present sufficient evidence to indicate a difference between the variabilities of the closing prices of the two stocks for the populations associated with the two samples? Give
An experiment is conducted to compare two new automobile designs. Twenty people are randomly selected, and each person is asked to rate each design on a scale of 1 (poor) to 10 (excellent). The resulting ratings will be used to test the null hypothesis that the mean level of approval is the same
The data shown here were collected on lost-time accidents (the figures given are mean work-hours lost per month over a period of 1 year) before and after an industrial safety program was put into effect. Data were recorded for six industrial plants. Do the data provide sufficient evidence to
Organic chemists often purify organic compounds by a method known as fractional crystallization. One chemist prepared ten 4.85-g quantities of aniline and purified it to acetanilide. The following dry yields were recorded:Estimate the mean grams of acetanilide that can be recovered from an initial
To compare the demand for two different entrees, the manager of a cafeteria recorded the number of purchases of each entree on seven consecutive days. The data are shown in the table. Do the data provide sufficient evidence to indicate a greater mean demand for one of the entrees? Use the Excel
The EPA limit on the allowable discharge of suspended solids into rivers and streams is 60 milligrams per liter (mg/l) per day. A study of water samples selected from the discharge at a phosphate mine shows that over a long period, the mean daily discharge of suspended solids is 48 mg/l, but
Two methods were used to measure the specific activity (in units of enzyme activity per milligram of protein) of an enzyme. One unit of enzyme activity is the amount that catalyzes the formation of 1 micromole of product per minute under specified conditions. Use an appropriate test or estimation
A producer of machine parts claimed that the diameters of the connector rods produced by his plant had a variance of at most .03 inch2. A random sample of 15 connector rods from his plant produced a sample mean and variance of .55 inch and .053 inch2, respectively. a. Is there sufficient evidence
How much sleep do you get on a typical school night? A group of 10 college students were asked to report the number of hours that they slept on the previous night with the following results:a. Find a 99% confidence interval for the average number of hours that college students sleep. b. What
The following data are the response times in seconds for n = 25 first graders to arrange three objects by size.Find a 95% confidence interval for the average response time for first graders to arrange three objects by size. Interpret this interval.
Want to attend a pro-basketball finals game? The average prices for the NBA rematch of the Boston Celtics and the LA Lakers in 2010 compared to the average ticket prices in 2008 are given in the table that follows.a. If we were to assume that the prices given in the table have been randomly
An article in American Demographics investigated consumer habits at the mall. We tend to spend the most money shopping on the weekends, and, in particular, on Sundays from 4 to 6 P.M. Wednesday morning shoppers spend the least! Suppose that a random sample of 20 weekend shoppers and a random sample
As part of a larger pilot study, students at a Riverside, California middle school, will compare the learning of algebra by students using iPads versus students using the traditional algebra textbook with the same author and publisher. To remove teacher-to-teacher variation, the same teacher will
Refer to Exercise 10.11. Approximately how many 4.85-g specimens of aniline are required if you wish to estimate the mean number of grams of acetanilide correct to within .06 g with probability equal to .95?Exercise 10.11Organic chemists often purify organic compounds by a method known as
In a study to determine which factors predict who will benefit from treatment for bulimia nervosa, an article in the British Journal of Clinical Psychology indicates that self-esteem was one of these important predictors. The table gives the mean and standard deviation of self-esteem scores prior
Here are the red blood cell counts (in 106 cells per micro liter) of a healthy person measured on each of 15 days:Find a 95% confidence interval estimate of m, the true mean red blood cell count for this person during the period of testing.

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