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

Each part of this problem specifies a claim about a population proportion, the sample size n, and the desired level of significance a. Formulate (i) the hypotheses, (ii) the test statistic, and (iii) the rejection region. (The answers to part (a) are provided for illustration.)(i) H0: p = .32 H1: p
(a)
A manager of a campus store that sells posters conjectures that more than 30% of all freshman dorm rooms have a poster of a rock group. From n = 60 rooms selected at random, an investigator records X = number of rooms having a poster of a rock group. (a) Formulate a null and alternative hypotheses
When estimating μ from a large sample, suppose that one has found the 95% error margin of X to be 4.2. From this information, determine: (a) The estimated S.E. of . (b) The 90% error margin.
An educator wishes to test H0: p = .3 against H1: p > .3, where p = proportion of college football players who graduate in four years. (a) State the test statistic and the rejection region for a large sample test having α = .05. (b) If 19 out of a random sample of 48 players graduated in four
A concerned group of citizens wants to show that less than half the voters support the President's handling of a recent crisis. Let p = proportion of voters who support the handling of the crisis. (a) Determine H0 and H1. (b) If a random sample of 500 voters gives 228 in support, what does the test
Refer to Exercise 8.61. Perform a test of hypotheses to determine whether the proportion of ERS calls involving flat tires or lockouts was significantly smaller than .19, the true proportion for previous years. (Use a 5% level of significance.)
Refer to Example 12 where n = 5000 and proportion .78 of the students sometimes use cell phones while driving. Conduce a test of hypotheses, of size .05, with the intent of establishing that the population proportion is greater than .75.
An independent bank concerned about its customer base decided to conduct a survey of bank customers. Out of 505 customers who returned the survey form, 258 rated the overall bank services as excellent. (a) Test, at level α = .10, the null hypothesis that the proportion of customers who would rate
With reference to Exercise 8.74, (a) Find a 90% confidence interval for the proportion of customers who would rate the overall bank services as excellent. (b) The bank has 8200 customers. Convert your confidence interval for the proportion in part (a) into a 90% confidence interval for the total
From telephone interviews with 980 adults, it was found that 78% of those persons supported tougher legislation for antipollution measures. Does this poll substantiate the conjecture that more than 75% of the adult population are in favor of tougher legislation for antipollution measures? (Answer
Refer to the box with the smiling face scale for rating cereals on page 339. Using the data that 30 out of 42 youngsters in a sample rated a cereal in the highest category, find an approximate 95% confidence interval for the corresponding population proportion.
Refer to Exercise 2.4 where the number of automobile accidents reported per month were recorded for an intersection. The sample size is n = 59, = 1.949, and s = 1.558 accidents.(a) Give a point estimate of μ, the mean number of accidents reported per month.(b) Determine the estimated standard
A student in a large lecture section asked students how much they paid for a used copy of the text. The n = 38 responses yieldedExi = 3230.84 dollars ∑(xi - )2 = 2028.35(a) Give a point estimate of μ, the mean price paid.(b) Determine the estimated standard error.(c) Calculate the 95% error
The same owners operate two coffee shops in a large building. One is (a) small and the other (b) large. On any day, the number of customers is only observed for one shop. Determine the point estimate of μ, the mean number of persons served during a weekday morning, and the 100(1 - a)% error
The time it takes for a taxi to drive from the office to the airport was recorded on 40 occasions. It was found that = 47 minutes and 5 = 5 minutes. Give (a) An estimate of μ = population mean time to drive. (b) An approximate 95.4% error margin.
By what factor should the sample size be increased to reduce the standard error of to (a) One-half its original value? (b) One-fourth its original value?
A food service manager wants to be 95% certain that the error in the estimate of the mean number of sandwiches dispensed over the lunch hour is 10 or less. What sample size should be selected if a preliminary sample suggests (a) σ = 40? (b) σ = 80?
A zoologist wishes to estimate the mean blood sugar level of a species of animal when injected with a specified dosage of adrenaline. A sample of 55 animals of a common breed are injected with adrenaline, and their blood sugar measurements are recorded in units of milligrams per 100 milliliters of
Refer to Exercise 2.3 and the data on the number of extracurricular activities in which 30 students participated in the past week. These data have n = 30 = 1.925 s = 1.607 activities (a) Obtain a 98% confidence interval for μ, the population mean number of activities. (b) In a long series of
After feeding a special diet to 80 mice, the scientist measures their weight in grams and obtains = 35 grams and 5 = 4 grams. He states that a 90% confidence interval for Î¼ is given by(a) Was the confidence interval calculated correctly? If not, provide the correct result. (b) Does
The amount of PCBs was measured in 40 samples of soil that were treated with contaminated sludge. The following summary statistics were obtained. = 3.56 s = .5 ppm (a) Perform a test of hypotheses with the intent of establishing that the mean PCB contamination is less than 3.7 p.p.m. Take α =
In each case, identify the null hypothesis (H0) and the alternative hypothesis (H1) using the appropriate symbol for the parameter of interest. (a) A consumer group plans to test-drive several cars of a new model in order to document that its average highway mileage is less than 50 miles per
A literary critic wants to establish that the mean number of words per sentence, appearing in a newly discovered short story, is different from 9.1 words. A sample of 36 sentences provided the data = 8.6 and s = 1.2 (a) Formulate the null and alternative hypotheses. (Define any symbols you
A test will be" conducted to see how long a seven-ounce tube of toothpaste lasts. The researcher wants to establish that the mean time is greater than 30.5 days. From a random sample of size 75, an investigator obtains = 32.3 and s = 6.2 days.(a) Formulate the null and alternative hypotheses.
When estimating the mean of a population, how large a sample is required in order that the 95% error margin be: (a) 1/8 of the population standard deviation? (b) 15% of the population standard deviation?
In a given situation, suppose H0 was rejected at α = .05. Answer the following questions as "yes," "no," or "can't tell" as the case may be. (a) Would H0 also be rejected at α = .03? (b) Would H0 also be rejected at α = .10? (c) Is the P-value larger than .05?
Refer to the data on the amount of reflected light from urban areas in Table D.3b of the Data Bank. A computer calculation for a test of H0: u = 84 versus H1: Î¼ ‰ 84 has the outputTest of mu = 84 vs mu not = 84(a) What is the conclusion of the test when Î± =
Refer to Example 6 where, one day, the visits of n = 48 students to the social network site produced the summary statistics = 35.96 minutes and s = 29.11 minutes n = 48 (a) Calculate a 90% confidence interval for the mean daily time spent on the social network site. (b) Compare your interval with
The daily number of kayaks sold, X, at a water sports store has the probability distribution(a) Find the expected number of kayaks sold in a day.(b) Find the standard deviation of the number of kayaks sold in a day.(c) Suppose data from the next 64 different days give = .84 and standard deviation
In a large-scale, cost-of-living survey undertaken last January, weekly grocery expenses for families with one or two children were found to have a mean of $148 and a standard deviation of $25. To investigate the current situation, a random sample of families with one or two children is to be
In 2011, 67% of persons 22-33 years old held passports. From a random sample of size n = 84 collected today, 64 are passport holders. (a) Estimate the proportion of persons 22-33 years old who hold passports today. (b) Estimate a 95% error margin for your estimate.
With reference to Exercise 8.95, (a) Conduct a test of size .05 with the intent of establishing that the proportion today is larger than .67. (b) Find a 95% confidence interval for that proportion.
Out of a sample of n = 625 students interviewed, 139 had missed at least one class last week. Obtain a 95% confidence interval for p = proportion of all students that missed at least one class last week.
With reference to Exercise 8.97, conduct a test with the intent of establishing that p > .20. (a) Formulate the null and alternative hypotheses. (b) Determine the test statistic. (c) Give the form of the rejection region. (d) What is the conclusion to your test? Take α = .05. (e) Calculate a
From May 15 through June 30, 2012, American Airlines flew 152 flights from Chicago, Illinois, to Austin, Texas. Of these, 22 arrived late. Treat this as a random sample and conduct a test with the intent of establishing that the population proportion of late flights is greater than .10. (a)
Using the table for the t distributions, find: (a) The upper .05 point when d.f. = 6. (b) The lower .025 point when d.f. = 10. (c) The lower .01 point when d.f. = 9. (d) The upper .10 point when d.f. = 13.
Recorded here are the germination times (number of days) for seven seeds of a new strain of snap bean.Stating any assumptions that you make, determine a 95% confidence interval for the true mean germination time for this strain.
A zoologist collected 20 wild lizards in the southwestern United States. The total length (mm) of each was measured.Obtain a 95% confidence interval for the mean length.
One approach to investigating the consequences of a major oil spill in the Gulf of Mexico is to look at the amount of heavy metals that have been incorporated in the shells of oysters. Oysters continually build their shells, and if vanadium, cobalt, or chromium from the oil are incorporated in the
Eighteen samples of seaweed, each weighing 50-kilograms, are collected to study the feasibility of extracting protein for use in animal feed. The 18 determinations of protein yield have sample mean 3.6 kilograms and standard deviation .8 kilogram. Determine a 95% confidence interval for the mean
The monthly rent (dollars) for a two-bedroom apartment on the west side of town was recorded for a sample of ten apartments.Obtain a 95% confidence interval for the mean monthly rent for two-bedroom apartments.
From a random sample of size 12, one has calculated the 95% confidence interval for p and obtained the result (38.6, 46.2). (a) What are the x and s for that sample? (b) Calculate a 98% confidence interval for μ.
From a random sample of size 18, a researcher states that (11.1, 15.7) inches is a 90% confidence interval for p, the mean length of bass caught in a small lake. A normal distribution was assumed. Using the 90% confidence interval, obtain: (a) A point estimate of p and its 90% margin of error. (b)
Henry Cavendish (1731-1810) provided direct experimental evidence of Newton's law of universal gravitation, which specifies the force of attraction between two masses. In an experiment with known masses determined by weighing, the measured force can also be used to calculate a value for the density
Henry Cavendish (1731-1810) provided direct experimental evidence of Newton's law of universal gravitation, which specifies the force of attraction between two masses. In an experiment with known masses determined by weighing, the measured force can also be used to calculate a value for the density
One of the first investigations of the amount of persistent organic pollutants present in soil within an urban setting was motivated by a major flood seventy days earlier.1 One series of measurements of the total amount of PCB congeners consisted of 14 observations measured in the units ng g-1 d.w.
Refer to Exercise 9.18. Do these data support the claim that the mean logarithm of the amount of PCB congeners is less than 3.8? Take α = .05.
Name the t percentiles shown and find their values from Appendix B, Table 5.
Refer to Exercise 9.14. Do these data support the claim that the mean monthly rent for a two-bedroom apartment differs from 775 dollars? Take α = .05.
The data on the lengths of anacondas on the front piece of the chapter yield a 95% confidence interval for the population mean length of all anaconda snakes in the area of the study.(a) Is the population mean length of all female anacondas living in the study area contained in this interval? (b)
Refer to the data on the weight (pounds) of male wolves given in Table D.9 of the Data Bank. A computer calculation gives a 95% confidence interval.(a) Is the population mean weight for all male wolves in the Yukon-Charley Rivers National Reserve contained in this interval? (b) Explain why you are
The following measurements of the diameters (in feet) of Indian mounds in southern Wisconsin were gathered by examining reports in Wisconsin Archeologist (courtesy of J. Williams).(a) Do these data substantiate the conjecture that the population mean diameter is larger than 21 feet? Test at Î± =
Measurements of the acidity (pH) of rain samples were recorded at 13 sites in an industrial region.Determine a 95% confidence interval for the mean acidity of rain in that region.
Refer to Exercise 9.11, where a zoologist collected 20 wild lizards in the southwestern United States. Do these data substantiate a claim that the mean length is greater than 128 mm? Test with α = .05.
Geologists dating rock, using a strontium-isotope technique, provided the ages 5.2 and 4.4 million years for two specimens. Treating these as a random sample of size 2 from a normal distribution(a) Obtain a 90% confidence interval for p, the true age of the rock formation.(b) Geologists do get an
The data on the weight (lb) of female wolves, from Table D.9 of the Data Bank, areTest the null hypothesis that the mean weight of females is 83 pounds versus a two-sided alternative. Take Î± = .05.
The ability of a grocery store scanner to read accurately is measured in terms of maximum attenuation (db). In one test with 20 different products, the values of this measurement had a mean 10.7 and standard deviation 2.4. The normal assumption is reasonable.(a) Is there strong evidence that p, the
The mean drying time of a brand of spray paint is known to be 90 seconds. The research division of the company that produces this paint contemplates that adding a new chemical ingredient to the paint will accelerate the drying process. To investigate this conjecture, the paint with the chemical
Using the table for the t distributions find: (a) The 90th percentile of the r distribution when d.f. = 8. (b) The 99th percentile of the f distribution when d.f. = 5. (c) The 5th percentile of the f distribution when d.f. = 22. (d) The lower and upper quartiles of the t distribution when d.f. = 17.
A few years ago, noon bicycle traffic past a busy section of campus had a mean of μ = 300. To see if any change in traffic has occurred, counts were taken for a sample of 15 weekdays. It was found that = 340 and s = 30.(a) Construct an α = .05 test of H0: μ = 300 against the alternative that
Refer to the computer anxiety scores for female accounting students in Table D.4 of the Data Bank. A computer calculation for a test of H0: Î¼ = 2 versus H1: Î¼ ‰ 2 is given here.(a) What is the conclusion if you test with a = .05? (b) What mistake could you
Based on a random sample of tail lengths for 15 male kites, an investigator calculates the 95% confidence interval (183.0, 195.0) mm based on the t distribution. The normal assumption is reasonable. (a) What is the conclusion of the t test for H0: μ = 190.5 versus H1: μ ≠ 190.5? (b) What is the
In Example 3, the 90% confidence interval for the mean weight of female wolves was found to be (67.13, 80.62) pounds. (a) What is the conclusion of testing H0: μ = 81 versus H1: μ ≠ 81 at level α = .10? (b) What is the conclusion if H0: μ = 69?
The petal width (mm) of one kind of iris has a normal distribution. Suppose that, from a random sample of widths, the t based 90% confidence interval for the population mean width is (16.8, 19.6) mm. Answer each question "yes," "no," or "can't tell," and justify your answer. On the basis of the
Recorded here are the amounts of decrease in percent of body fat for eight participants in an exercise program over three weeks.(a) Construct a 95% confidence interval for the population mean amount p of decrease in percent body fat over the three-week program.(b) If you were to test H0: p = 15
Refer to the data in Exercise 9.35.(a) Construct a 90% confidence interval for μ.(b) If you were to test H0: μ = 10 versus H1: μ ≠ 10 at α = .10, what would you conclude from your result in part (a)? Why?(c) Perform the hypothesis test indicated in part (b) and confirm your conclusion.
Establish the connection between the large sample Z test, which rejects H0: Î¼ = Î¼0 in favor of H1: Î¼ ‰ Î¼0, at Î± = .05, ifand the 95% confidence interval
Using the table for the x2 distributions, find: (a) The upper 5% point when d.f. = 9. (b) The upper 1% point when d.f. = 14. (c) The lower 2.5% point when d.f. = 7. (d) The lower 1% point when d.f. = 22.
Name the x2 percentiles shown and find their values from Appendix B, Table 6.(a)(b) (c) Find the percentile in part (a) if d.f. = 40. (d) Find the percentile in part (b) if d.f. = 8.
Find the probability of (a) T < -1.761 when d.f. = 14. (b) |T| > 2.306 when d.f. = 8. (c) -1.738 < T < 1.734 when d.f. = 18. (d) -1.812 < T < 2.764 when d.f. = 10.
Find the probability of (a) x2 > 31.33 when d.f. = 18. (b) x2 > 1.15 when d.f. = 15. (c) 3.24 < x2 > 18.31 when d.f. = 10. (d) 3.49 < x2 > 20.09 when d.f. = 10.
Beginning students in accounting took a test and a computer anxiety score (CARS) was assigned to each student on the basis of their answers to nineteen questions on the test (see Table D.4 of the Data Bank). A small population standard deviation would indicate that computer anxiety is nearly the
Find a 90% confidence interval for σ based on the n = 40 measurements of heights of red pine seedlings given in Exercise 8.4. State any assumption you make about the population. (s = .475 for this data set.)
Refer to Exercise 9.42. A related species has population standard deviation σ = .6. Do the data provide strong evidence that the red pine population standard deviation is smaller than .6? Test with α = .05.
Plastic sheets produced by a machine are periodically monitored for possible fluctuations in thickness. Uncontrollable heterogeneity in the viscosity of the liquid mold makes some variation in thickness measurements unavoidable. However, if the true standard deviation of thickness exceeds 1.5
Refer to Exercise 9.44. Construct a 95% confidence interval for the true standard deviation of the thickness of sheets produced on this shift.In Exercise 9.44Plastic sheets produced by a machine are periodically monitored for possible fluctuations in thickness. Uncontrollable heterogeneity in the
During manufacture, the thickness of laser printer paper is monitored. Data from several random samples each day during the year suggest that thickness follows a normal distribution. A sample of M = 10 thickness measurements (ten-thousandths inch) yields the 95% confidence interval (4.33, 11.50)
Refer to the data of lizard lengths in Exercise 9.11. (a) Determine a 90% confidence interval for the population standard deviation a. (b) Should H0: σ = 9 be rejected in favor of H1: σ ≠ 9 at α = .10? [Answer by using your result in part (a).]
Referring to the data in Exercise 9.17, determine a 99% confidence interval for the population standard deviation of the density measurements.
Referring to Exercise 9.23, construct a 95% confidence interval for the population standard deviation of the diameters of Indian mounds.
In each case, find the number b so that (a) P[T < b] = .95 when d.f. = 7. (b) P[-b < T < b] = .95 when d.f. = 16. (c) P[T > b] = .01 when d.f. = 5. (d) P[T > b] = .99 when d.f. = 11.
Do the data in Exercise 9.24 substantiate the conjecture that the true standard deviation of the acidity measurements is larger than 0.4? Test at α = .05.
Using the table of percentage points for the distributions, find (a) t.05 when d.f. = 7. (b) t.025 when d.f. = 11. (c) The lower .05 point when d.f. = 7. (d) The lower .05 point when d.f. = 11.
Using the table for the t distributions, find the probability of (a) T > 2.720 when d.f. = 22. (b) T < 3.250 when d.f. = 9. (c) |T| < 2.567 when d.f. = 17. (d) -1.383 < T < 2.262 when d.f. = 9.
A t distribution assigns more probability to large values than the standard normal. (a) Find t.05 for d.f. = 12 and then evaluate P[Z > t.05]. Verify that P[T > t.05] is greater than P[Z > t.05]. (b) Examine the relation for d.f. of 5 and 20, and comment.
Measurements of the amount of suspended solids in river water on 14 Monday mornings yield = 47 and s = 9.4 mg/1. Obtain a 95% confidence interval for the mean amount of suspended solids. State any assumption you make about the population.
Determine a 99% confidence interval for p using the data in Exercise 9.54.
The time to blossom of 21 plants has = 38.4 days and s = 5.1 days. Give a 95% confidence interval for the mean time to blossom.
Refer to Example 8 concerning the product volume for green gasoline. Obtain (a) A point estimate of p and its 95% error margin. (b) A 90% confidence interval for the mean. (c) Explain why you are 90% confident that the interval in part (b) covers the true unknown mean.
Refer to Exercise 9.54. The water quality is acceptable if the mean amount of suspended soilds is less than 49 mg/1. Construct an α = .05 test to establish that the quality is acceptable. (a) Specify H0 and H1. (b) State the test statistic. (c) What does the test conclude?
Refer to Exercise 9.56. Do these data provide strong evidence that the mean time to blossom is less than 42 days? Test with α = .01. (a) Formulate the null and alternative hypotheses. (b) Determine the test statistic. (c) Give the form of the rejection region. (d) What is the conclusion to your
Record the t.05 values for d.f. of 5, 10, 15, 20, and 29. Does this percentile increase or decrease with increasing degrees of freedom?
In a study of head injuries to ice hockey players the number of hits were monitored electronically by equipping approved helmets with accelerometers that measured head acceleration (m/s2) when a player was hit. The researches counted the number of serious hits, those greater than 30 m/s2,
Referring to Exercise 9.60, test H0: μ = 2.8 versus H1: μ ≠ 2.8 using α = .02.
Refer to Example 8 concerning the yield of green gasoline. Conduct a test of hypothesis which is intended to show that the mean product volume is greater than 2.75 liters.(a) Formulate the null and alternative hypotheses.(b) Determine the test statistic.(c) Give the form of the rejection region.(d)
The supplier of a particular brand of vitamin pills claims that the average potency of these pills after a certain exposure to heat and humidity is at least 65. Before buying these pills, a distributor wants to verify the supplier's claim is valid. To this end, the distributor chooses a random
A weight loss program advertises "LOSE 40 POUNDS IN 4 MONTHS." A random sample of n = 25 customers has = 32 pounds lost and s = 12. To contradict this claim test H0: μ = 40 against H1: μ < 40 with α = .05.
A car advertisement asserts that with the new collapsible bumper system, the average body repair cost for the damages sustained in a collision impact of 10 miles per hour does not exceed $1500. To test the validity of this claim, 5 cars are crashed into a stone barrier at an impact force of 10
Combustion efficiency measurements were recorded for 10 home heating furnaces of a new model. The sample mean and standard deviation were found to be 73.2 and 2.74, respectively. Do these results provide strong evidence that the average efficiency of the new model is higher than 70? (Test at α =

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