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Introductory Statistics 8th Edition Prem S. Mann - Solutions

A survey of 500 randomly selected adult men showed that the mean time they spend per week watching sports on television is 9.75 hours with a standard deviation of 2.2 hours. Construct a 90% confidence interval for the population mean, µ.
A random sample of 300 female members of health clubs in Los Angeles showed that they spend, on average, 4.5 hours per week doing physical exercise with a standard deviation of .75 hour. Find a 98% confidence interval for the population mean.
A computer company that recently developed a new software product wanted to estimate the mean time taken to learn how to use this software by people who are somewhat familiar with computers. A random sample of 12 such persons was selected. The following data give the times taken (in hours) by these
A company that produces 8-ounce low-fat yogurt cups wanted to estimate the mean number of calories for such cups. A random sample of 10 such cups produced the following numbers of calories.Construct a 99% confidence interval for the population mean. Assume that the numbers of calories for such cups
For a data set obtained from a sample, n = 20 and x̅. It is known that σ = 3.1. The population is normally distributed.a. What is the point estimate of µ?b. Make a 99% confidence interval for µ.c. What is the margin of error of estimate for part b?
An insurance company selected a sample of 50 auto claims filed with it and investigated those claims carefully. The company found that 12% of those claims were fraudulent.a. What is the point estimate of the percentage of all auto claims filed with this company that are fraudulent?b. Make a 99%
A casino player has grown suspicious about a specific roulette wheel. Specifically, this player believes that the slots for the numbers 0 and 00, which can lead to larger payoffs, are slightly smaller than the rest of 36 slots, which means that the ball would land in these two slots less often than
A sample of 20 managers was taken, and they were asked whether or not they usually take work home. The responses of these managers are given below, where yes indicates they usually take work home and no means they do not.Make a 99% confidence interval for the percentage of all managers who take
Salaried workers at a large corporation receive 2 weeks’ paid vacation per year. Sixteen randomly selected workers from this corporation were asked whether or not they would be willing to take a 3% reduction in their annual salaries in return for 2 additional weeks of paid vacation. The following
A researcher wants to determine a 99% confidence interval for the mean number of hours that adults spend per week doing community service. How large a sample should the researcher select so that the estimate is within 1.2 hours of the population mean? Assume that the standard deviation for time
An economist wants to find a 90% confidence interval for the mean sale price of houses in a state. How large a sample should she select so that the estimate is within $3500 of the population mean? Assume that the standard deviation for the sale prices of all houses in this state is $31,500.
A large city with chronic economic problems is considering legalizing casino gambling. The city council wants to estimate the proportion of all adults in the city who favor legalized casino gambling. What is the most conservative estimate of the sample size that would limit the margin of error to
Refer to Exercise 8.116. Assume that a preliminary sample has shown that 63% of the adults in this city favor legalized casino gambling. How large should the sample size be so that the 95% confidence interval for the population proportion has a margin of error of .05?
Let µ be the hourly wage (excluding tips) for workers who provide hotel room service in a large city. A random sample of a number (more than 30) of such workers yielded a 95% confidence interval for µ of $8.46 to $9.86 using the normal distribution with a known population standard deviation.a.
In April 2012, N3L Optics conducted a telephone poll of 1080 adult Americans aged 18 years and older. One of the questions asked respondents to identify which outdoor activities and sports they favor for fitness. Respondents could choose more than one activity/sport. Of the respondents, 76% said
For a data set obtained from a sample, n = 81 and . It is known that σ = 4.8. a. What is the point estimate of µ? b. Make a 95% confidence interval for µ. c. What is the margin of error of estimate for part b?
A group of veterinarians wants to test a new canine vaccine for Lyme disease. (Lyme disease is transmitted by the bite of an infected deer tick.) In an area that has a high incidence of Lyme disease, 100 dogs are randomly selected (with their owners’ permission) to receive the vaccine. Over a
When one is attempting to determine the required sample size for estimating a population mean, and the information on the population standard deviation is not available, it may be feasible to take a small preliminary sample and use the sample standard deviation to estimate the required sample size,
A gas station attendant would like to estimate p, the proportion of all households that own more than two vehicles. To obtain an estimate, the attendant decides to ask the next 200 gasoline customers how many vehicles their households own. To obtain an estimate of p, the attendant counts the number
A couple considering the purchase of a new home would like to estimate the average number of cars that go past the location per day. The couple guesses that the number of cars passing this location per day has a population standard deviation of 170. a. On how many randomly selected days should the
The U.S. Senate just passed a bill by a vote of 55€“45 (with all 100 senators voting). A student who took an elementary statistics course last semester says, €œWe can use these data to make a confidence interval about p. We have n = 100 and pÌ‚ = 55/100 =
When calculating a confidence interval for the population mean µ with a known population standard deviation σ, describe the effects of the following two changes on the confidence interval: (1) Doubling the sample size, (2) Quadrupling (multiplying by 4) the sample size. Give two reasons why this
At the end of Section 8.2, we noted that we always round up when calculating the minimum sample size for a confidence interval for µ with a specified margin of error and confidence level. Using the formula for the margin of error, explain why we must always round up in this situation.
Calculating a confidence interval for the proportion requires a minimum sample size. Calculate a confidence interval, using any confidence level of 90% or higher, for the population proportion for each of the following. a. n = 200 and p̂ = .01 b. n = 160 and p̂ = .9875 Explain why these
The standard deviation for a population is σ = 15.3. A sample of 36 observations selected from this population gave a mean equal to 74.8. a. Make a 90% confidence interval for µ. b. Construct a 95% confidence interval for µ. c. Determine a 99% confidence interval for µ. d. Does the width of the
The standard deviation for a population is σ = 14.8. A sample of 25 observations selected from this population gave a mean equal to 143.72. The population is known to have a normal distribution. a. Make a 99% confidence interval for µ. b. Construct a 95% confidence interval for µ. c. Determine a
The standard deviation for a population is σ = 6.30. A random sample selected from this population gave a mean equal to 81.90. The population is known to be normally distributed. a. Make a 99% confidence interval for µ assuming n = 16. b. Construct a 99% confidence interval for µ assuming n =
The standard deviation for a population is σ = 7.14. A random sample selected from this population gave a mean equal to 48.52. a. Make a 95% confidence interval for µ assuming n = 196. b. Construct a 95% confidence interval for µ assuming n = 100. c. Determine a 95% confidence interval for µ
For a population, the value of the standard deviation is 2.65. A sample of 35 observations taken from this population produced the following data.a. What is the point estimate of µ? b. Make a 98% confidence interval for µ. c. What is the margin of error of estimate for part b?
For a population, the value of the standard deviation is 4.96. A sample of 32 observations taken from this population produced the following data.a. What is the point estimate of µ? b. Make a 99% confidence interval for µ. c. What is the margin of error of estimate for part b?
For a population data set, σ = 12.5 a. How large a sample should be selected so that the margin of error of estimate for a 99% confidence interval for µ is 2.50? b. How large a sample should be selected so that the margin of error of estimate for a 96% confidence interval for µ is 3.20?
Explain the meaning of a point estimate and an interval estimate.
For a population data set, σ = 14.50. a. What should the sample size be for a 98% confidence interval for µ to have a margin of error of estimate equal to 5.50? b. What should the sample size be for a 95% confidence interval for µ to have a margin of error of estimate equal to 4.25?
Determine the sample size for the estimate of µ for the following. a. E = 2.3, σ = 15.40, confidence level = 99% b. E = 4.1, σ = 23.45, confidence level = 95% c. E = 25.9, σ = 122.25, confidence level = 90%
Determine the sample size for the estimate of for the following. a. E = .17, σ = .90, confidence level = 99% b. E = 1.45, σ = 5.82, confidence level = 95% c. E = 5.65, σ = 18.20, confidence level = 90%
A travel agent wants to gather information on the per-night cost at hotels in Caribbean countries. She took a random sample of 52 rooms from various hotels in those countries. The sample produced a mean cost for the 52 rooms to be $208.35 per night. If the population standard deviation of costs for
A city planner wants to estimate the average monthly residential water usage in the city. He selected a random sample of 40 households from the city, which gave the mean water usage to be 3415.70 gallons over a 1-month period. Based on earlier data, the population standard deviation of the monthly
An entertainment company is in the planning stages of producing a new computer-animated movie for national release, so they need to determine the production time (labor-hours necessary) to produce the movie. The mean production time for a random sample of 14 big-screen computer-animated movies is
Lazurus Steel Corporation produces iron rods that are supposed to be 36 inches long. The machine that makes these rods does not produce each rod exactly 36 inches long. The lengths of the rods vary slightly. It is known that when the machine is working properly, the mean length of the rods made on
At Farmer’s Dairy, a machine is set to fill 32-ounce milk cartons. However, this machine does not put exactly 32 ounces of milk into each carton; the amount varies slightly from carton to carton. It is known that when the machine is working properly, the mean net weight of these cartons is 32
A consumer agency that proposes that lawyers’ rates are too high wanted to estimate the mean hourly rate for all lawyers in New York City. A sample of 70 lawyers taken from New York City showed that the mean hourly rate charged by them is $570. The population standard deviation of hourly charges
A bank manager wants to know the mean amount of mortgage paid per month by homeowners in an area. A random sample of 120 homeowners selected from this area showed that they pay an average of $1575 per month for their mortgages. The population standard deviation of such mortgages is $215. a. Find a
A marketing researcher wants to find a 95% confidence interval for the mean amount that visitors to a theme park spend per person per day. She knows that the standard deviation of the amounts spent per person per day by all visitors to this park is $11. How large a sample should the researcher
A company that produces detergents wants to estimate the mean amount of detergent in 64-ounce jugs at a 99% confidence level. The company knows that the standard deviation of the amounts of detergent in all such jugs is .20 ounce. How large a sample should the company select so that the estimate is
A department store manager wants to estimate at a 98% confidence level the mean amount spent by all customers at this store. The manager knows that the standard deviation of amounts spent by all customers at this store is $31. What sample size should he choose so that the estimate is within $3 of
Refer to Exercise 8.24. A city planner wants to estimate, with a 97% confidence level, the average monthly residential water usage in the city. Based on earlier data, the population standard deviation of the monthly residential water usage in this city is 389.60 gallons. How large a sample should
You are interested in estimating the mean commuting time from home to school for all commuter students at your school. Briefly explain the procedure you will follow to conduct this study. Collect the required data from a sample of 30 or more such students and then estimate the population mean at a
You are interested in estimating the mean age of cars owned by all people in the United States. Briefly explain the procedure you will follow to conduct this study. Collect the required data on a sample of 30 or more cars and then estimate the population mean at a 95% confidence level. Assume that
Briefly explain the similarities and the differences between the standard normal distribution and the t distribution.
What are the parameters of a normal distribution and a t distribution? Explain.
Briefly explain the meaning of the degrees of freedom for a t distribution. Give one example.
What assumptions must hold true to use the t distribution to make a confidence interval for µ?
Explain the various alternatives for decreasing the width of a confidence interval. Which is the best alternative?
Find the value of t for the t distribution for each of the following. a. Area in the right tail = .05 and df = 12 b. Area in the left tail = .025 and n = 66 c. Area in the left tail = .001 and df = 49 d. Area in the right tail = .005 and n = 24
a. Find the value of t for the t distribution with a sample size of 21 and area in the left tail equal to .10. b. Find the value of t for the t distribution with a sample size of 14 and area in the right tail equal to .025. c. Find the value of t for the t distribution with 45 degrees of freedom
For each of the following, find the area in the appropriate tail of the t distribution. a. t = 2.467 and df = 28 b. t = –1.672 and df = 58 c. t = –2.670 and n = 55 d. t = 2.819 and n = 23
For each of the following, find the area in the appropriate tail of the t distribution. a. t = –1.302 and df = 42 b. t = 2.797 and n = 25 c. t = 1.397 and n = 9 d. t = –2.383 and df = 67
Find the value of t from the t distribution table for each of the following. a. Confidence level = 99% and df = 13 b. Confidence level = 95% and n = 36 c. Confidence level = 90% and df = 16
a. Find the value of t from the t distribution table for a sample size of 22 and a confidence level of 95%. b. Find the value of t from the t distribution table for 60 degrees of freedom and a 90% confidence level. c. Find the value of t from the t distribution table for a sample size of 24 and a
A sample of 18 observations taken from a normally distributed population produced the following data:a. What is the point estimate of µ? b. Make a 99% confidence interval for µ. c. What is the margin of error of estimate for µ in part b?
A sample of 11 observations taken from a normally distributed population produced the following data:a. What is the point estimate of µ? b. Make a 95% confidence interval for µ. c. What is the margin of error of estimate for µ in part b?
Suppose, for a sample selected from a normally distributed population, 68.50 and s = 8.9. a. Construct a 95% confidence interval for µ assuming n = 16. b. Construct a 90% confidence interval for µ assuming n = 16. Is the width of the 90% confidence interval smaller than the width of the 95%
Suppose, for a sample selected from a population, = 25.5 and s = 4.9. a. Construct a 95% confidence interval for µ assuming n = 47. b. Construct a 99% confidence interval for µ assuming n = 47. Is the width of the 99% confidence interval larger than the width of the 95% confidence interval
Briefly explain how the width of a confidence interval decreases with an increase in the sample size. Give an example.
a. A sample of 100 observations taken from a population produced a sample mean equal to 55.32 and a standard deviation equal to 8.4. Make a 90% confidence interval for µ b. Another sample of 100 observations taken from the same population produced a sample mean equal to 57.40 and a standard
a. A sample of 400 observations taken from a population produced a sample mean equal to 92.45 and a standard deviation equal to 12.20. Make a 98% confidence interval for µ b. Another sample of 400 observations taken from the same population produced a sample mean equal to 91.75 and a standard
A random sample of 16 airline passengers at the Bay City airport showed that the mean time spent waiting in line to check in at the ticket counters was 31 minutes with a standard deviation of 7 minutes. Construct a 99% confidence interval for the mean time spent waiting in line by all passengers at
A random sample of 20 acres gave a mean yield of wheat equal to 41.2 bushels per acre with a standard deviation of 3 bushels. Assuming that the yield of wheat per acre is normally distributed, construct a 90% confidence interval for the population mean µ.
Almost all employees working for financial companies in New York City receive large bonuses at the end of the year. A sample of 65 employees selected from financial companies in New York City showed that they received an average bonus of $55,000 last year with a standard deviation of $18,000.
According to the 2010 Time Use Survey conducted by the U.S. Bureau of Labor Statistics, Americans of age 15 years and older spent an average of 164 minutes per day watching TV in 2010 (USA TODAY, June 23, 2011). Suppose a recent sample of 25 people of age 15 years and older selected from a city
The high price of medicines is a source of major expense for those seniors in the United States who have to pay for these medicines themselves. A random sample of 2000 seniors who pay for their medicines showed that they spent an average of $4600 last year on medicines with a standard deviation of
Jack’s Auto Insurance Company customers sometimes have to wait a long time to speak to a customer service representative when they call regarding disputed claims. A random sample of 25 such calls yielded a mean waiting time of 22 minutes with a standard deviation of 6 minutes. Construct a 99%
A random sample of 36 mid-sized cars tested for fuel consumption gave a mean of 26.4 miles per gallon with a standard deviation of 2.3 miles per gallon. a. Find a 99% confidence interval for the population mean, µ. b. Suppose the confidence interval obtained in part a is too wide. How can the
The mean time taken to design a house plan by 40 architects was found to be 23 hours with a standard deviation of 3.75 hours. a. Construct a 98% confidence interval for the population mean . b. Suppose the confidence interval obtained in part a is too wide. How can the width of this interval be
Briefly explain how the width of a confidence interval decreases with a decrease in the confidence level. Give an example.
The following data give the speeds (in miles per hour), as measured by radar, of 10 cars traveling on Interstate I-15:Assuming that the speeds of all cars traveling on this highway have a normal distribution, construct a 90% confidence interval for the mean speed of all cars traveling on this
A company randomly selected nine office employees and secretly monitored their computers for one month. The times (in hours) spent by these employees using their computers for non€“job-related activities (playing games, personal communications, etc.) during this month are as
A dentist wants to find the average time taken by one of her hygienists to take X-rays and clean teeth for patients. She recorded the time to serve 24 randomly selected patients by this hygienist. The data (in minutes) are as follows:Assume that such times for this hygienist for all patients are
A businesswoman is considering whether to open a coffee shop in a local shopping center. Before making this decision, she wants to know how much money people spend per week at coffee shops in that area. She took a random sample of 26 customers from the area who visit coffee shops and asked them to
A random sample of 34 participants in a Zumba dance class had their heart rates measured before and after a moderate 10-minute workout. The following data correspond to the increase in each individual€™s heart rate (in beats per minute):a. What is the point estimate of the corresponding
The following data give the number of pitches thrown by both teams in each of a random sample of 24 Major League Baseball games played between the beginning of the 2012 season and May 16, 2012.a. Create a histogram of these data using the class intervals 210 to less than 230, 230 to less than 250,
You are working for a supermarket. The manager has asked you to estimate the mean time taken by a cashier to serve customers at this supermarket. Briefly explain how you will conduct this study. Collect data on the time taken by any supermarket cashier to serve 40 customers. Then estimate the
You are working for a bank. The bank manager wants to know the mean waiting time for all customers who visit this bank. She has asked you to estimate this mean by taking a sample. Briefly explain how you will conduct this study. Collect data on the waiting times for 45 customers who visit a bank.
What assumption(s) must hold true to use the normal distribution to make a confidence interval for the population proportion, p?
Check if the sample size is large enough to use the normal distribution to make a confidence interval for p for each of the following cases. a. n = 50 and p̂ = .25 b. n = 160 and p̂ = .03 c. n = 400 and p̂ = .65 d. n = 75 and p̂ = .06
Check if the sample size is large enough to use the normal distribution to make a confidence interval for p for each of the following cases. a. n = 80 and p̂ = .85 b. n = 110 and p̂ = .98 c. n = 35 and p̂ = .40 d. n = 200 and p̂ = .08
a. A sample of 300 observations taken from a population produced a sample proportion of .63. Make a 95% confidence interval for p. b. Another sample of 300 observations taken from the same population produced a sample proportion of .59. Make a 95% confidence interval for p. c. A third sample of 300
a. A sample of 1100 observations taken from a population produced a sample proportion of .32. Make a 90% confidence interval for p. b. Another sample of 1100 observations taken from the same population produced a sample proportion of .36. Make a 90% confidence interval for p. c. A third sample of
A sample of 200 observations selected from a population produced a sample proportion equal to .91. a. Make a 90% confidence interval for p. b. Construct a 95% confidence interval for p. c. Make a 99% confidence interval for p. d. Does the width of the confidence intervals constructed in parts a
A sample of 200 observations selected from a population gave a sample proportion equal to .27. a. Make a 99% confidence interval for p. b. Construct a 97% confidence interval for p. c. Make a 90% confidence interval for p. d. Does the width of the confidence intervals constructed in parts a through
A sample selected from a population gave a sample proportion equal to .73. a. Make a 99% confidence interval for p assuming n = 100. b. Construct a 99% confidence interval for p assuming n = 600. c. Make a 99% confidence interval for p assuming n = 1500. d. Does the width of the confidence
A sample selected from a population gave a sample proportion equal to .31. a. Make a 95% confidence interval for p assuming n = 1200. b. Construct a 95% confidence interval for p assuming n = 500. c. Make a 95% confidence interval for p assuming n = 80. d. Does the width of the confidence intervals
a. How large a sample should be selected so that the margin of error of estimate for a 99% confidence interval for p is .035 when the value of the sample proportion obtained from a preliminary sample is .29? b. Find the most conservative sample size that will produce the margin of error for a 99%
a. How large a sample should be selected so that the margin of error of estimate for a 98% confidence interval for p is .045 when the value of the sample proportion obtained from a preliminary sample is .53? b. Find the most conservative sample size that will produce the margin of error for a 98%
Briefly explain how the width of a confidence interval decreases with a decrease in the confidence level. Give an example. Discuss.
Determine the most conservative sample size for the estimation of the population proportion for the following. a. E = .025, confidence level = 95% b. E = .05, confidence level = 90% c. E = .015, confidence level = 99%
Determine the sample size for the estimation of the population proportion for the following, where p̂ is the sample proportion based on a preliminary sample. a. E = .025, p̂ = .16, confidence level = 95% b. E = .05, p̂ = .85, confidence level = 90% c. E = .015, p̂ = .97, confidence level = 99%
According to a Pew Research Center nationwide telephone survey of adults conducted March 15 to April 24, 2011, 55% of college graduates said that their college education prepared them for a job (Time, May 30, 2011). Suppose that this survey included 1450 college graduates. a. What is the point
The express check-out lanes at Wally’s Supermarket are limited to customers purchasing 12 or fewer items. Cashiers at this supermarket have complained that many customers who use the express lanes have more than 12 items. A recently taken random sample of 200 customers entering express lanes at
According to a Pew Research Center nationwide telephone survey of adults conducted March 15 to April 24, 2011, 69% of college graduates said that their college education gave them maturity (Time, May 30, 2011). Suppose that this survey included 1450 college graduates. a. What is the point estimate

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