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mathematics
statistics

Questions and Answers of Statistics

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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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?
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
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
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
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,
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
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
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
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
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
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
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
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.
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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

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