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

Refer to the model for monthly differences in the exchange rate shown in Figure 9. Calculate the mean and variance of the number of times, in two years, that the absolute value of a one-month difference exceeds (a) .048 (b) .072
Refer to the Statistics in Context section concerning the flower importer. (a) Suppose it takes the importer two months to pay his invoices. Proceed by taking the sum of the adjacent one-month differences to obtain the two-month differences. Make a histogram of these differences two months apart.
The population density function and that for the sampling distribution of , for n = 2, are shown in Figure 10. Identify which one is the sampling distribution and explain your answer.Figure 11 Two density functions. Exercise 7.36.
A population consists of the four numbers {0, 2, 4, 6}. Consider drawing a random sample of size 2 with replacement.(a) List all possible samples and evaluate x for each.(b) Determine the sampling distribution of .(c) Write down the population distribution and calculate its mean p and standard
Refer to Exercise 7.38 and, instead of , consider the statisticSample range R = Largest observation - Smallest observationFor instance, if the sample observations are (2, 6), the range is 6 - 2 = 4.(a) Calculate the sample range for all possible samples.(b) Determine the sampling distribution of R.
Explain why the following collection procedures are likely to produce data that fail to yield the desired information. (a) To evaluate public opinion about a new global trade agreement, an interviewer asks persons, "Do you feel that this unfair trade agreement should be canceled?" (b) To determine
What sample size is required in order that the standard deviation of be: (a) 1/4 of the population standard deviation? (b) 1/7 of the population standard deviation? (c) 12% of the population standard deviation?
A population has distributionValue Probability1.............................22............................ .63............................ .2Let X1 and X2 be independent and each have the same distribution as the population.(a) Determine the missing elements in the table for the sampling
A population has distributionValue Probability1........................63....................... .35........................1Let X1 and X2 be independent and each have the same distribution as the population.(a) Determine the missing elements in the table for the sampling distribution of = (X1 +
Suppose the weights of the contents of cans of mixed nuts have a normal distribution with mean 32.4 ounces and standard deviation .4 ounce. For a random sample of size n = 9(a) What are the mean and standard deviation of ?(b) What is the distribution of ? Is this distribution exact or
The weights of pears in an orchard are normally distributed with mean .32 pound and standard deviation .08 pound. (a) If one pear is selected at random, what is the probability that its weight is between .28 and .34 pound? (b) If denotes the average weight of a random sample of four pears, what
Suppose that the size of pebbles in a river bed is normally distributed with mean 12.1mm and standard deviation 3.2 mm. A random sample of 9 pebbles are measured. Let denote the average size of the sampled pebbles.(a) What is the distribution of ?(b) What is the probability that is smaller
A random sample of size 150 is taken from the population of the ages of juniors enrolled at a large university during one semester. This population has mean 21.1 years and standard deviation 2.6. The population distribution is not normal.(a) Is it reasonable to assume a normal distribution for the
A company that manufactures car mufflers finds that the labor to set up and run a nearly automatic machine has mean μ = 1.9 hours and σ = 1.2 hours. For a random sample of 36 runs(a) Determine the mean and standard deviation of .(b) What can you say about the distribution of ?
Refer to Exercise 7.47. Evaluate (a) P[ > 2.2] (b) P[1.65 < < 2.25]
Visitors to a popular Internet site rated the newest gaming console on a scale of 1 to 5 stars. The following probability distribution is proposed based on over 1400 individual ratings. f(x)1........................022....................... .023.......................
From the set of numbers {3, 5, 7}, a random sample of size 2 is selected with replacement. (a) List all possible samples and evaluate x for each. (b) Determine the sampling distribution of X.
A special purpose coating must have the proper abrasion. The standard deviation is known to be 21. Consider a random sample of 49 abrasion measurements.(a) Find the probability that the sample mean lies within 2 units of the population mean-that is, P[-2 < - μ < 2].(b) Find the number k
The daily number of kayaks sold, X, at a water sports store has the probability distribution align="center">(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) Find the probability distribution of the total number of
Suppose packages of cream cheese coming from an automated processor have weights that are normally distributed. For one day's production run, the mean is 8.2 ounces and the standard deviation is 0.1 ounce. (a) If the packages of cream cheese are labeled 8 ounces, what proportion of the packages
Suppose the amount of sun block lotion in plastic bottles leaving a filling machine has a normal distribution. The bottles are labeled 300 milliliters (ml) but the actual mean is 302 ml and the standard deviation is 2 ml. (a) What is the probability that an individual bottle contains less than 299
A random sample of size 2 is selected, with replacement, from the set of numbers {0, 2, 4}. (a) List all possible samples and evaluate x and s2 for each. (b) Determine the sampling distribution of X. (c) Determine the sampling distribution of s2.
To determine the time a cashier spends on a customer in the express lane, the manager decides to record the time to check-out for the customer who is being served at 10 past the hour, 20 past the hour, and so on. Will measurements collected in this manner be a random sample of the times a cashier
Using a physical device to generate random samples. Using a die, generate a sample and evaluate the statistic. Then repeat many times and obtain an estimate of the sampling distribution. In particular, investigate the sampling distribution of the median for a sample of size 3 from the population
A researcher wants to estimate p, the mean number of minutes before a person scores over 200 on a new computer game. She wishes to get estimates, separately, for each of the groups (a) novices, (b) occasional game players, and (c) expert game players. When using to estimate p find the (i)
Assume that the standard deviation of the number of violent incidents in one hour of children's shows on television is 3.2. An investigator would like to be 99% sure that the true mean number of violent incidents per hour is estimated within 1.4 incidents. For how many randomly selected hours does
Each year, an insurance company reviews its claim experience in order to set future rates. Regarding their damage-only automobile insurance policies, at least one claim was made on 2073 of the 12,299 policies in effect for the year. Treat these data as a random sample for the population of all
A genetic model suggests that 80% of the plants grown from a cross between two given strains of seeds will be of the dwarf variety. After breeding 200 of these plants, 136 were observed to be of the dwarf variety. (a) Does this observation strongly contradict the genetic model? (b) Construct a 95%
Internet prices for glasses are often considerably lower than those at the brick and mortar stores but quality is another question. To address that issue, some optometrists ordered 154 adult pairs of spectacles from various online stores.6 Of the 154 pairs of spectacles, 44 pairs of eye wear
A researcher asked participants to wear a simple counting device for a week and, for each day, to count the number of times they thought about food.7 The average of the seven daily counts, for each of n = 65 participants, are summarized by the statistics n = 65 = 19.22 s = 17.66 Find a 95%
Consider the problem of testing H0: Î¼ = 10 versus H1: Î¼ > 10 with n = 64, Ïƒ = 2 (known), and Î± = .025. The rejection region of this test is given bySuppose we wish to calculate the power of this test at the alternative Î¼1 = 11.
Refer to the data on the computer attitude score (CAS) in Table D.4 of the Data Bank. A computer summary of a level Î± = .05 test of H0: Î¼ = 2.6 versus a two-sided alternative and a 95% confidence interval is given below.(a) Will the 99% confidence interval for mean CAS
Refer to the data on percent malt extract in Table D.8 of the Data Bank. A computer summary of a level a = .05 test of H0: p = 77 versus a two-sided alternative and a 95% confidence interval is given below.(a) Will the 98% confidence interval for mean malt extract be smaller or larger than the one
Refer to the data on the heights of red pine seedlings in Exercise 8.4. Use MINITAB (or some other package program) to:(a) Find a 97% percent confidence interval for the mean height.(b) Test H0: μ = 1.9 versus H1: μ ≠ 1.9 centimeters with α = .03.
Referring to speedy lizard data in Exercise 2.19, obtain a 95% confidence interval for the mean speed of that genus.
Refer to the male salmon data given in Table D.7 of the Data Bank. Use MINITAB or some other package program to find a 90% large sample confidence interval for the mean freshwater growth.
Referring to Exercise 8.5, suppose that the survey of 50 contested items was, in fact, a pilot study intended to give an idea of the population standard deviation. Assuming a = $25, determine the sample size that is needed for estimating the population mean amount contested with a 98% error margin
Refer to the physical fitness data given in Table D.5 of the Data Bank. Use MINITAB or some other package program to:(a) Find a 97% large sample confidence interval for the pretest number of situps.(b) Construct a histogram to determine if the underlying distribution is symmetric or has a long tail
Refer to the sleep data given in Table D.10 of the Data Bank. Use MINITAB or some other package program to:(a) Find a 95% large sample confidence interval for the mean number of breathing pauses per hour (BPH).(b) Construct a histogram to determine if the underlying distribution is symmetric or has
Refer to the grizzly bear data given in Table D.6 of the Data Bank. Use MINITAB or some other package program to:(a) Find a 95% large sample confidence interval for the mean weight in pounds of all bears living in that area.(b) Construct a histogram to determine if the underlying distribution is
Assume that the standard deviation of the heights of five-year-old boys is 3.5 inches. How many five-year-old boys need to be sampled if we want to be 90% sure that the population mean height is estimated within .5 inch?
Let the abbreviation PSLT stand for the percent of the gross family income that goes into paying state and local taxes. Suppose one wants to estimate the mean PSLT for the population of all families in New York City with gross incomes in the range $70,000 to $80,000. If σ = 2.5, how many such
To estimate μ with a 90% error margin of 2.9 units, one has determined that the required sample size is 108. What then is the required sample size if one wants the 95% error margin to be 1.8 units?
Refer to Example 4, Chapter 2, on page 29. Table 2 records the number of items returned by 30 persons to a large discount department store in late December. The summary statistics are n = 30, = 2.538, s = 1.303 Obtain a 98% confidence interval for μ, the population mean number of items
A company wants to check the consistency of electronic copies of signatures for consumer credit purchases. A sample of 49 electronic signatures are available from the same customer. One measure of consistency in signing is the total length that the script is outside the signature box. The sample of
Each day of the year, a large sample of cellular phone calls is selected and a 95% confidence interval is calculated for the mean length of all cellular phone calls on that day. Of these 365 confidence intervals, one for each day of the year, approximately how many will cover their respective
A forester measures 100 needles off a pine tree and finds = 3.1 centimeters and s = 0.7 centimeter. She reports that a 95% confidence interval for the mean needle length is(a) Is the statement correct? (b) Does the interval (2.96, 3.24) cover the true mean? Explain.
In a study on the nutritional qualities of fast foods, the amount of fat was measured for a random sample of 35 hamburgers of a particular restaurant chain. The sample mean and standard deviation were found to be 30.2 and 3.8 grams, respectively. Use these data to construct a 95% confidence
A researcher asked participants to wear a simple counting device for a week and they counted the number of times that they thought about food.2 Determine a point estimate of the daily mean number of times a person thinks about food and the (1 - a )% error margin separately for males and
In the same study described in Exercise 8.19, the sodium content was also measured for the sampled hamburgers, and the sample mean and standard deviation were 658 and 47 milligrams, respectively. Determine a 98% confidence interval for the true mean sodium content.
An entomologist sprayed 120 adult Melon flies with a specific low concentration of malathion and observed their survival times. The mean and standard deviation were found to be 18.3 and 5.2 days, respectively. Use these data to construct a 99% confidence interval for the true mean survival time.
Students are asked about the number of songs they downloaded from a pay-for-songs Web site the last month. From a random sample of 39 students, the sample mean was 4.7 with a standard deviation of 3.2.(a) Obtain a 95% confidence interval for μ, the mean number of songs downloaded by the population
The freshness of produce at a superstore is rated on a scale of 1 to 5 with 5 being very fresh. From a random sample of 49 customers, the average score was 3.8 with a standard deviation of .7.(a) Obtain a 95% confidence interval for the population mean, p, the mean score for the distribution of all
Referring to Example 7, where the 158 times to complete the firefighter test have mean 307.77 and standard deviation 51.852, obtain a 99% confidence interval for the mean time of all possible recruits who would complete the test.
Based on a survey of 140 employed persons in a city, the mean and standard deviation of the commuting distances between home and the principal place of business are found to be 8.6 and 4.3 miles, respectively. Determine a 90% confidence interval for the mean commuting distance for the population of
A manager at a power company monitored the employee time required to process high-efficiency lamp bulb rebates. A random sample of 40 applications gave a sample mean time of 3.8 minutes and a standard deviation of 1.2 minutes. Construct a 90% confidence interval for the mean time to process a.
A credit company randomly selected 50 contested items and recorded the dollar amount being contested. These contested items had a sample mean = 95.74 dollars and s = 24.63 dollars. Construct a 95% confidence interval for the mean amount contested, μ.
In a study to determine whether a certain stimulant produces hyperactivity, 55 mice were injected with 10 micrograms of the stimulant. Afterward, each mouse was given a hyperactivity rating score. The mean score was = 14.9 and s = 2.8. Give a 95% confidence interval for the population mean score
Refer to the Statistics in Context section of Chapter 7 concerning monthly changes in the Canadian to U.S. exchange rate. A computer calculation gives = -.0021 and s = .0234 for the n = 41 monthly changes. Find a 95% confidence interval for the mean monthly change.
During 2010, the Wisconsin Department of Natural Resources captured 10 male wolves and 6 female wolves which they weighed, radio collared, and released. (a) Female n = 6 = 63.6 pounds ∑ (xi - )2 = 333.5 (b) Male n = 10 = 79.4 pounds ∑(xi - )2 = 409.4 Obtain
An employee of an on-campus copy center wants to determine the mean number of copies before a cartridge needs to be replaced. She records the life length in thousands of copies for 43 cartridges and obtainsn = 43 = 8.12 s = 1.78 thousand copiesObtain a 90% confidence interval for the population
Refer to the 40 height measurements given in Exercise 8.4, which haven = 40 = 1.715 s = .475 centimeterCalculate a 99% confidence interval for the population mean height.
Radiation measurements on a sample of 65 microwave ovens produced = .11 and s = .06. Determine a 95% confidence interval for the mean radiation.
Refer to the data on the growth of female salmon in the marine environment in Table D.7 of the Data Bank. A computer calculation gives a 95% confidence interval.(a) Does the 95% confidence interval cover the true mean growth of all female salmon in that marine environment? (b) Why are you 95%
Refer to the data on the girth, in centimeters, of grizzly bears in Table D.6 of the Data Bank. A computer calculation gives(a) Does the 95% confidence interval cover the true mean girth of all grizzly bears in the area of the study? Explain. (b) Why are you 95% confident that the interval (87.93,
The amount of PCBs (polychlorinated biphenyls) 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) Obtain a 95% confidence interval for the population mean μ, amount of PCBs in the soil. Answer parts
A national fast food chain, with thousands of franchise locations, needed to audit the books at each location. They first selected a sample of 50 locations and performed the audit. They determined that a 95% confidence interval for the mean time to complete an audit is (28.4 hours, 52.7
Stated here are some claims or research hypotheses that are to be substantiated by sample data. In each case, identify the null hypothesis H0 and the alternative hypothesis H\ in terms of the population mean p. (a) The mean time a health insurance company takes to pay claims is less than 14 working
From an analysis of the sample data, suppose that the decision has been to reject the null hypothesis. In the context of each part (a-d) of Exercise 8.37, answer the following questions: (a) In what circumstance is it a correct decision? (b) When is it a wrong decision, and what type of error is
From an analysis of the sample data, suppose that the decision has been made to retain the null hypothesis. In the context of each part (a-d) of Exercise 8.37, answer the following questions. (a) In what circumstance is it a correct decision? (b) When is it a wrong decision, and what type of error
To study the growth of pine trees at an early stage, a nursery worker records 40 measurements of the heights (cm) of one-year-old red pine seedlings, (courtesy of Professor Alan Ek)The summary statistics are n = 40 = 1.715 s = .475 centimeter
For each situation (a-d) in Exercise 8.37, state which of the following three forms of the rejection region is appropriate when Ïƒ is known.
Each part (a-d) of this problem gives the population standard deviation a, the statement of a claim about p, the sample size n, and the desired level of significance a. Formulate (i) the hypotheses, (ii) the test statistic Z, and (iii) the rejection region. (The answers to part (a) are
Suppose that the "observed values of the sample mean in the contexts of parts (a-d ) of Exercise 8.41 are given as follows. Calculate the test statistic Z and state the conclusion with the specified a.(a) = 30.54(b) = .136(c) = 77.35(d) x = -.59
A market researcher wants to perform a test with the intent of establishing that his company's medium pump bottle of soap has a mean life greater than 40 days. The sample size is 70 and he knows that σ = 5.6.(a) If you set the rejection region to be R: > 41.31, what is the level of
With reference to Exercise 8.15, perform a test with the intent of establishing that the mean number of items returned is greater than 2.0. Take a = .02.
With reference to Exercise 8.44, (a) Test H0: μ = 2.0 H1: μ ≠ 2.0 with α = .02. (a) What error could you have possibly made? (b) Based on your decision in part Explain in the context of the problem.
An investigator at a large midwestern university wants to determine the typical weekly amount of time students work on part-time jobs. More particularly, he wants to test the null hypothesis that the mean time is 15 hours versus a two-sided alternative. A sample of 39 students who hold part-time
Refer to the data on the growth of female salmon in the marine environment in Table D.7 of the Data Bank. A computer calculation for a test of H0: Î¼ = 411 versus H1: Î¼ ‰ 411 is given below.Test of mu = 411 vs mu not = 411(a) What is the conclusion if you test
Refer to the data on the girth, in centimeters, of grizzly bears in Table D.6 of the Data Bank. A computer calculation for a test of H0: Î¼ = 100 centimeters versus H1: Î¼ ‰ 100 givesOne-Sample Z: GirthTest of mu = 100 vs mu not = 100(a) What is the conclusion
A manager at a power company monitored the employee time required to process high-efficiency lamp bulb rebates. A random sample of 40 applications gave a sample mean time of 3.8 minutes and a standard deviation of 1.2 minutes. (a) Is the claim that μ > 3.5 minutes substantiated by these data? Test
A credit company randomly selected 50 contested items and recorded the dollar amount being contested. These contested items had sample mean = 95.74 dollars and s = 24.63 dollars. Construct a point estimate for the population mean contested amount, p, and give its 90% error margin.
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 d = 29.11 minutes n = 48 (a) Conduct a test of hypotheses with the intent of establishing that mean connect time is greater than 30 minutes. Take α =
A company wants to establish that the mean life of its batteries, when used in a wireless mouse, is over 183 days. The data consist of the life lengths of batteries in 64 different wireless mice.(a) Formulate the null and alternative hypotheses.(b) What is the conclusion to your test if = 190.5
In a given situation, suppose H0 was not rejected at α = .02. Answer the following questions as "yes," "no," or "can't tell" as the case may be. (a) Would H0 also be retained at α = .01? (b) Would H0 also be retained at α = .05? (c) Is the P-value smaller than .02?
A company wishing to improve its customer service collected hold times from 75 randomly selected incoming calls to its hot line that were put on hold. These calls had sample mean hold time = 3.4 minutes and s = 2.4 minutes. Is the claim that μ > 3.0 minutes substantiated by these data? Test with
A company's mixed nuts are sold in cans and the label says that 25% of the contents is cashews. Suspecting that this might be an overstatement, an inspector takes a random sample of 35 cans and measures the percent weight of cashews [i.e., 100 (weight of cashews/weight of all nuts)] in each can.
Biological oxygen demand (BOD) is an index of pollution that is monitored in the treated effluent of paper mills on a regular basis. From 43 determinations of BOD (in pounds per day) at a particular paper mill during the spring and summer months, the mean and standard deviation were found to be
Refer to Exercise 8.55. Along with the determinations of BOD, the discharge of suspended solids (SS) was also monitored at the same site. The mean and standard deviation of the 43 determinations of SS were found to be 5710 and 1720 pounds per day, respectively. Do these results strongly support the
Suppose that n units are randomly sampled and x number of the sampled units are found to have the characteristic of interest. In each case, (i) define p in the context of the problem, (ii) provide a point estimate of p and (iii) determine the 95% error margin.5 (a) A survey is conducted of n = 986
Software programs using artificial intelligence are now writing many stories. These so called robots have replaced humans as the authors of routine reports in sports, finance, and other areas. During the first seven days of September 2012, the football pages on the Big Ten network site contained 66
In a psychological experiment, individuals are permitted to react to a stimulus in one of two ways, say, A or B. The experimenter wishes to estimate the proportion p of persons exhibiting reaction A. How many persons should be included in the experiment to be 90% confident that the error of
A manager at a power company monitored the employee time required to process high-efficiency lamp bulb rebates. A random sample of 40 applications gave a sample mean time of 3.8 minutes and a standard deviation of 1.2 minutes. Construct a point estimate for the population mean time to process, p,
A national safety council wishes to estimate the proportion of automobile accidents that involve pedestrians. How large a sample of accident records must be examined to be 98% certain that the estimate does not differ from the true proportion by more than .03? (The council believes that the true
An automobile club that pays for emergency road services (ERS) requested by its members wishes to estimate the proportions of the different types of ERS requests. Upon examining a sample of 2927 ERS calls, it finds that 1499 calls related to starting problems, 849 calls involved serious mechanical
Each year, an insurance company reviews its claim experience in order to set future rates. Regarding their damage-only automobile insurance policies, at least one claim was made on 2073 of the 12,299 policies in effect for the year. Treating these data as a random sample for the population of all
Out of a sample of 94 purchases at the drive-up window of a fast-food establishment, 27 were made with a major credit card. (a) Estimate the proportion of sales made with a credit card. (b) Obtain the estimated standard error. (c) Find a 98% confidence interval for the population proportion of
Refer to Example 16 and the babies born to parents that both smoke. (a) Find a 90% confidence interval for the proportion of male babies born to parents that both smoke. (b) Does p lie in your interval obtained in part(a)? (c) Why are you 95% confident about your interval in part(a)?
Identify the null and the alternative hypotheses in the following situations. (a) A university official believes that the proportion of students who currently hold part-time jobs has increased from the value .26 that prevailed four years ago. (b) A cable company claims that, because of improved
Given here are the descriptive statements of some claims that one intends to establish on the basis of data. In each case, identify the null and the alternative hypotheses in terms of a population proportion p. (a) Of smokers who eventually quit smoking, less than 40% are able to do so in just one

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