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mathematics
statistics

Questions and Answers of Statistics

These data are the weights (in pounds) of 27 packages of ground beef in a supermarket meat display:a. Interpret the accompanying MINITAB printouts for the one-sample test and estimation
The serum cholesterol levels of 50 subjects randomly selected from the L.A. Heart Data, data from an epidemiological heart disease study on Los Angeles County employees, follow.a. Construct a
Refer to Exercise 10.16. Since n 30, use the methods of Chapter 8 to create a large-sample 95% confidence interval for the average serum cholesterol level for L.A. County employees. Compare the two
Give the number of degrees of freedom for s2, the pooled estimator of σ2, in these cases: a. n1 = 16, n2 = 8 b. n1 = 10, n2 = 12 c. n1 = 15, n2 = 3
Calculate s2, the pooled estimator for s2, in these cases: a. n1 = 10, n2 = 4, s21 = 3.4, s22 = 4.9 a. n1 = 12, n2 = 21, s21 = 18, s22 = 23
Find the critical value(s) of t that specify the rejection region in these situations: a. A two-tailed test with α = .01 and 12 df b. A right-tailed test with α = .05 and 16 df c. A two-tailed test
Two independent random samples of sizes n1 = 4 and n2 = 5 are selected from each of two normal populations:a. Calculate s2, the pooled estimator of s2.b. Find a 90% confidence interval for (µ1 -
Independent random samples of n1 = 16 and n2 = 13 observations were selected from two normal populations with equal variances:a. Suppose you wish to detect a difference between the population means.
Refer to Exercise 10.21. Find a 99% confidence interval for (µ1 - µ2).Exercise 10.21Independent random samples of n1 = 16 and n2 = 13 observations were selected from two normal
The MINITAB printout shows a test for the difference in two population means.Two-Sample T-Test and CI: Sample 1, Sample 2Two-sample T for Sample 1 vs Sample 2Difference = mu (Sample 1) - mu (Sample
The MS Excel printout shows a test for the difference in two population means.a. Do the two sample variances indicate that the assumption of a common population variance is reasonable?b. What is the
Jan Lindhe conducted a study on the effect of an oral antiplaque rinse on plaque buildup on teeth. Fourteen people whose teeth were thoroughly cleaned and polished were randomly assigned to two
In Exercise 10.6 we presented data on the estimated average price for a 6-ounce can or a 7.06-ounce pouch of tuna, based on prices paid nationally in supermarkets. A portion of the data is reproduced
Chronic anterior compartment syndrome is a condition characterized by exercise-induced pain in the lower leg. Swelling and impaired nerve and muscle function also accompany this pain, which is
An experiment published in The American Biology Teacher studied the efficacy of using 95% ethanol or 20% bleach as a disinfectant in removing bacterial and fungal contamination when culturing plant
A geologist collected 20 different ore samples, all of the same weight, and randomly divided them into two groups. The titanium contents of the samples, found using two different methods, are listed
Use Table 4 in Appendix I to approximate the p-value for the t statistic in each situation: a. A two-tailed test with t = 2.43 and 12 df b. A right-tailed test with t = 3.21 and 16 df c. A two-tailed
The numbers of raisins in each of 14 mini boxes (1/2-ounce size) were counted for a generic brand and for Sun maid® brand raisins:a. Although counts cannot have a normal distribution, do these data
Refer to Exercise 10.7, in which we measured the dissolved oxygen content in river water to determine whether a stream had sufficient oxygen to support aquatic life. A pollution control inspector
In an effort to compare the average swimming times for two swimmers, each swimmer was asked to swim freestyle for a distance of 100 yards at randomly selected times. The swimmers were thoroughly
Refer to Exercise 10.32. Construct a lower 95% one-sided confidence bound for the difference in the average times for the two swimmers. Does this interval confirm your conclusions in Exercise
How does Aaron Rodgers, quarterback for the 2011 Super Bowl Champion Green Bay Packers, compare to Drew Brees, quarterback for the 2010 Super Bowl winners, the New Orleans Saints? The table below
An article in Archaeometry involved an analysis of 26 samples of Romano-British pottery, found at four different kiln sites in the United Kingdom. The samples were analyzed to determine their
A paired-difference experiment was conducted using n = 10 pairs of observations.a. Test the null hypothesis H0: (µ1 - µ2) = 0 against Ha: (µ1 - µ2) ≠ 0 for α = .05, = .3, and s2d = .16. Give
A paired-difference experiment consists of n = 18 pairs, = 5.7, and s2d = 256. Suppose you wish to detect µd > 0. a. Give the null and alternative hypotheses for the test. b. Conduct the test and
A paired-difference experiment was conducted to compare the means of two populations:a. Do the data provide sufficient evidence to indicate that µ1 differs from µ2? Test using Î± = .05.b. Find
In Exercise 2.4, we presented the annual 2010 premium for a male, licensed for 6-8 years, who drives a Honda Accord 12,600 to 15,000 miles per year and has no violations or accidents.a. Why would you
The test scores on a 100-point test were recorded for 20 students:a. Can you reasonably assume that these test scores have been selected from a normal population? Use a stem and leaf plot to justify
Refer to Exercise 10.27. In addition to the compartment pressures, the level of creatine phosphokinase (CPK) in blood samples, a measure of muscle damage, was determined for each of 10 runners and 10
An advertisement for a popular supermarket chain claims that it has had consistently lower prices than one of its competitors. As part of a survey conducted by an independent price-checking company,
An experiment was conducted to compare the mean reaction times to two types of traffic signs: prohibitive (No Left Turn) and permissive (Left Turn Only). Ten drivers were included in the experiment.
The earth's temperature can be measured using either ground-based sensors or infrared-sensing devices mounted in aircraft or space satellites. Ground-based sensoring is very accurate but tedious,
To test the comparative brightness of two red dyes, nine samples of cloth were taken from a production line and each sample was divided into two pieces. One of the two pieces in each sample was
In response to a complaint that a particular tax assessor (A) was biased, an experiment was conducted to compare the assessor named in the complaint with another tax assessor (B) from the same
A psychology class performed an experiment to compare whether a recall score in which instructions to form images of 25 words were given is better than an initial recall score for which no imagery
Before contracting to have stereo music piped into each of his suites of offices, an executive had his office manager randomly select seven offices in which to have the system installed. The average
A random sample of n = 25 observations from a normal population produced a sample variance equal to 21.4. Do these data provide sufficient evidence to indicate that σ2 > 15? Test using α = .05.
The following n = 10 observations are a sample from a normal population:a. Find the mean and standard deviation of these data.b. Find a 99% upper one-sided confidence bound for the population mean
A random sample of n = 15 observations was selected from a normal population. The sample mean and variance were = 3.91 and s2 = .3214. Find a 90% confidence interval for the population variance σ2.
A random sample of size n = 7 from a normal population produced these measurements: 1.4, 3.6, 1.7, 2.0, 3.3, 2.8, 2.9. a. Calculate the sample variance, s2. b. Construct a 95% confidence interval for
A precision instrument is guaranteed to read accurately to within 2 units. A sample of four instrument readings on the same object yielded the measurements 353, 351, 351, and 355. a. Test the null
To properly treat patients, drugs prescribed by physicians must not only have a mean potency value as specified on the drug's container, but also the variation in potency values must be small.
Refer to Exercise 10.53. Testing of 60 additional randomly selected containers of the drug gave a sample mean and variance equal to 5.04 and .0063 (for the total of n = 64 containers). Using a 95%
A manufacturer of hard safety hats for construction workers is concerned about the mean and the variation of the forces helmets transmit to wearers when subjected to a standard external force. The
Refer to Exercise 10.55. Do the data provide sufficient evidence to indicate that s exceeds 40? Exercise 10.55 A manufacturer of hard safety hats for construction workers is concerned about the mean
A manufacturer of industrial light bulbs likes its bulbs to have a mean length of life that is acceptable to its customers and a variation in length of life that is relatively small.A sample of 20
Independent random samples from two normal populations produced the variances listed here:a. Do the data provide sufficient evidence to indicate that Ïƒ21 differs from Ïƒ22? Test using Î± =
Refer to Exercise 10.58 and find a 95% confidence interval for Ïƒ21/Ïƒ22.Exercise 10.58Independent random samples from two normal populations produced the variances listed here:
Is there a difference in the prices of tuna, depending on the method of packaging? Consumer Reports gives the estimated average price for a 6-ounce can or a 7.06-ounce pouch of tuna, based on prices
Independent random samples from two normal populations produced the given variances:a. Do the data provide sufficient evidence to indicate that Ïƒ21 Ïƒ22? Test using Î± = .05.b. Find the
The SAT subject tests in chemistry and physics for two groups of 15 students each electing to take these tests are given below.To use the two-sample t-test with a pooled estimate of Ïƒ2, you must
The stability of measurements on a manufactured product is important in maintaining product quality. A manufacturer of lithium batteries, such as the ones used for digital cameras, suspected that one
Quarterbacks not only need to have a good passing percentage, but they need to be consistent. That is, the variability in the number of passes completed per game should be small. The table below
In Exercise 10.26 and dataset EX1026, you conducted a test to detect a difference in the average prices of light tuna in water versus light tuna in oil. a. What assumption had to be made concerning
Refer to Exercise 10.27. Susan Beckham and colleagues conducted an experiment involving 10 healthy runners and 10 healthy cyclists to determine if there are significant differences in pressure
A pharmaceutical manufacturer purchases a particular material from two different suppliers. The mean level of impurities in the raw material is approximately the same for both suppliers, but the
What assumptions are made when Student's t-test is used to test a hypothesis concerning a population mean?
What assumptions are made about the populations from which random samples are obtained when the t distribution is used in making small-sample inferences concerning the difference in population means?
Why use paired observations to estimate the difference between two population means rather than estimation based on independent random samples selected from the two populations? Is a paired
Industrial wastes and sewage dumped into our rivers and streams absorb oxygen and thereby reduce the amount of dissolved oxygen available for fish and other forms of aquatic life. One state agency
Use Table 4 in Appendix I to find the following critical values: a. An upper one-tailed rejection region with α = .05 and 11 df. b. A two-tailed rejection region with α = .05 and 7 df. c. A lower
Use Table 4 in Appendix I to bound the following p-values:a. P(t > 1.2) with 5 dfb. P(t > 2) + P(t < - 2) with 5 df with 10 dfc. P(t < - 3.3) with 8 dfd. P(t > 0.6) with 12 df
A random sample of n = 12 observations from a normal population produced = 47.1 and s2 = 4.7. Test the hypothesis H0: µ = 48 against H0: µ ≠ 48 at the 5% level of significance.
A manufacturer can tolerate a small amount (.05 milligrams per liter (mg/l)) of impurities in a raw material needed for manufacturing its product. Because the laboratory test for the impurities is
The main stem growth measured for a sample of seventeen 4-year-old red pine trees produced a mean and standard deviation equal to 11.3 and 3.4 inches, respectively. Find a 90% confidence interval for
The object of a general chemistry experiment is to determine the amount (in milliliters) of sodium hydroxide (NaOH) solution needed to neutralize 1 gram of a specified acid. This will be an exact
Measurements of water intake, obtained from a sample of 17 rats that had been injected with a sodium chloride solution, produced a mean and standard deviation of 31.0 and 6.2 cubic centimeters (cm3),
An experimenter was interested in determining the mean thickness of the cortex of the sea urchin egg. The thickness was measured for n = 10 sea urchin eggs. These measurements were obtained:Estimate
A production plant has two complex fabricating systems, both of which are maintained at 2-week intervals. However, one system is twice as old as the other. The number of finished products fabricated
The data in the table are the diameters and heights of 10 fossil specimens of a species of small shellfish, Rotularia (Annelida) fallax, that were unearthed in a mapping expedition near the Antarctic
In a study of the infestation of the Thenus orientalis lobster by two types of barnacles, Octolasmis tridens and O. lowei, the carapace lengths (in millimeters) of 10 randomly selected lobsters
Refer to Exercise 10.79 and data set EX1079. Suppose you want to estimate the mean diameter of the fossil specimens correct to within 5 millimeters with probability equal to .95. How many fossils do
To test the effect of alcohol in increasing the reaction time to respond to a given stimulus, the reaction times of seven people were measured. After consuming 3 ounces of 40% alcohol, the reaction
Here are the prices per ounce of n = 13 different brands of individually wrapped cheese slices:Construct a 95% confidence interval estimate of the underlying average price per ounce of individually
An experiment was conducted to compare the mean lengths of time required for the bodily absorption of two drugs A and B. Ten people were randomly selected and assigned to receive one of the drugs.
Refer to Exercise 10.83. Suppose you wish to estimate the difference in mean times to absorption correct to within 1 minute with probability approximately equal to .95.a. Approximately how large a
The weights in grams of 10 males and 10 female juvenile ring-necked pheasants are given below.a. Use a statistical test to determine if the population variance of the weights of the male birds
Insects hovering in flight expend enormous amounts of energy for their size and weight. The data shown here were taken from a much larger body of data collected by T.M. Casey and colleagues. They
The calcium (Ca) content of a powdered mineral substance was analyzed 10 times with the following percent compositions recorded:a. Find a 99% confidence interval for the true calcium content of this
Karl Niklas and T.G. Owens examined the differences in a particular plant, Plantago Major L., when grown in full sunlight versus shade conditions. In this study, shaded plants received direct
A comparison of the precisions of two machines developed for extracting juice from oranges is to be made using the following data:a. Is there sufficient evidence to indicate that there is a
In a study of the effect of cigarette smoking on the carbon monoxide diffusing capacity (DL) of the lung, researchers found that current smokers had DL readings significantly lower than those of
Four sets of identical twins (pairs A, B, C, and D) were selected at random from a computer database of identical twins. One child was selected at random from each pair to form an "experimental
Eight obese persons were placed on a diet for 1 month, and their weights, at the beginning and at the end of the month, were recorded:Estimate the mean weight loss for obese persons when placed on
Many seniors are ordering their drugs online to take advantage of lower costs for these pharmacies. A random sample of nine online pharmacies was selected and the cost of a 10-mg Buspar (Buspirone)
Research psychologists measured the baseline breathing patterns-the total ventilation (in liters of air per minute) adjusted for body size-for each of n = 30 patients, so that they could estimate the
A comparison of reaction times (in seconds) for two different stimuli in a psychological word-association experiment produced the following results when applied to a random sample of 16 people:Do the
Refer to Exercise 10.94. Suppose that the word-association experiment is conducted using eight people as blocks and making a comparison of reaction times within each person; that is, each person is
Refer to Exercises 10.94 and 10.95. Calculate a 95% confidence interval for the difference in the two population means for each of these experimental designs. Does it appear that blocking increased
The following data are readings (in foot-pounds) of the impact strengths of two kinds of packaging material:MS Excel output a. Use the MS Excel printout to determine whether there is evidence of a
An experiment was conducted to compare the densities (in ounces per cubic inch) of cakes prepared from two different cake mixes. Six cake pans were filled with batter A, and six were filled with
Under what assumptions can the F distribution be used in making inferences about the ratio of population variances?
If you are a California resident, the API (Academic Performance Index) may be published by your local paper. The 2009-2010 accountability progress report for Riverside County, California, was
Suppose you wish to compare the means of six populations based on independent random samples, each of which contains 10 observations. Insert, in an ANOVA table, the sources of variation and their
A clinical psychologist wished to compare three methods for reducing hostility levels in university students using a certain psychological test (HLT). High scores on this test were taken to indicate
Refer to Exercise 11.10. Let Î¼A and Î¼B, respectively, denote the mean scores at the end of the semester for the populations of extremely hostile students who were treated throughout that
An experiment was conducted to compare the effectiveness of three training programs, A, B, and C, in training assemblers of a piece of electronic equipment. Fifteen employees were randomly assigned,
An ecological study was conducted to compare the rates of growth of vegetation at four swampy undeveloped sites and to determine the cause of any differences that might be observed. Part of the study
Water samples were taken at four different locations in a river to determine whether the quantity of dissolved oxygen, a measure of water pollution, varied from one location to another. Locations 1
Calcium The calcium content of a powdered mineral substance was analyzed five times by each of three methods, with similar standard deviations:Use an appropriate test to compare the three methods of

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