Review Exercises 10.54 and 10.55. Describe what happens to the confidence interval estimate when a. the standard deviation is equal to the value used to determine the sample size. b. the standard deviation is smaller than the one used to determine the sample size. c. the standard deviation is larger than the one used to determine the sample size.
> Xis normally distributed with mean 1,000 and standard deviation 250. What is the probability that X lies between 800 and 1, 100?
> Xis normally distributed with mean 250 and standard deviation 40. What value of X does only the top 15% exceed?
> Find z.28.
> Find z.065.
> Find z.03.
> Calculate the p-value of the test to determine that there is sufficient evidence to infer each research objective. Research objective: The population mean is less than 250. σ = 40, n = 70, x = 240
> calculate the value of the test statistic, set up the rejection region, determine the p-value, interpret the result, and draw the sampling distribution. H0: μ = 50 H1: μ < 50 σ = 15, n = 100, x = 48, α = .05
> Find the probabilities. P(Z < 1.65)
> Find the probability. P(Z < 1.61)
> The following is a graph of a density function. a. Determine the density function. b. Find the probability that X is greater than 10. c. Find the probability that X lies between 6 and 12. .10- 0- 20
> The following density function describes the random variable X. a. Graph the density function. b. Find the probability that X lies between 1 and 3. c. What is the probability that X lies between 4 and 8? d. Compute the probability that X is less than 7.
> The following function is the density function for the random variable X: a. Graph the density function. b. Find the probability that X lies between 2 and 4. c. What is the probability that X is less than 3? * - 1 fAx) = 1<x < 5 8 %3D 00
> Use a computer to find the following probabilities. a. P(F600, 800 > 1.1) b. P(F35, 100 > 1.3) c. P(F66, 148 > 2.1) d. P(F17, 37 > 2.8)
> Calculate the value of the test statistic, set up the rejection region, determine the p-value, interpret the result, and draw the sampling distribution. H0: μ = 70 H1: μ > 70 σ = 20, n = 100, x = 80, α = .01
> Use a computer to find the following probabilities. a. P(F7, 20 > 2.5) b. P(F18, 63 > 1.4) c. P(F34, 62 > 1.8) d. P(F200, 400 > 1.1)
> Use a computer to find the following values of F. a. F.01, 100, 150 b. F.05, 25, 125 c. F.01, 11, 33 d. F.05, 300, 800
> A random variable has the following density function. f(x) = 1 − .5x 0 < x < 2 a. Graph the density function. b. Verify that f(x) is a density function. c. Find P(X > 1). d. Find P(X < .5). e. Find P(X = 1.5).
> Use the F table (Table 6) to find the following values of F. a. F.025, 8, 22 b. F.05, 20, 30 c. F.01, 9, 18 d. F..025, 24, 10
> Use the F table (Table 6) to find the following values of F. a. F.05, 3, 7 b. F.05, 7, 3 c. F.025, 5, 20 d. F.01, 12, 60
> Use a computer to find the following probabilities. Pržso > 250) b. Рзб > 25) Przoo > 500) d. Pi20 > 100) a. с.
> Use a computer to find the following probabilities. P > 80) b. Pz00 > 125) P(ss > 60) d. P(xio00 > 450) a. с.
> Use a computer to find the following values of χ2. a. χ2 .99, 55 b. χ2 .05, 800 c. χ2 .99, 43 d. χ2 .10, 233
> Use a computer to find the following values of χ2. a. χ2 .25, 66 b. χ2 .40, 100 c. χ2 .50, 17 d. χ2 .10, 17
> Use the χ2 table (Table 5) to find the following values of χ2. a. χ2 .90, 26 b. χ2 .01, 30 c. χ2 .10, 1 d. χ2 .99, 80 Data from Table 5: TABLE 8.5 Critical Values of x35, a and x35
> Calculate the value of the test statistic, set up the rejection region, determine the p-value, interpret the result, and draw the sampling distribution. H0: μ = 100 H1: μ ≠ 100 σ = 10, n = 100, x = 100, α = .05
> Let X represent the result of the toss of a fair die. Find the following probabilities. a. P(X = 1) b. P(X = 6)
> Draw a diagram that shows the sampling distribution representing two unbiased estimators, one of which is relatively efficient.
> The random variable X is exponentially distributed with λ = 3. Sketch the graph of the distribution of X by plotting and connecting the points representing f(x) for x = 0, .5, 1, 1.5, and 2.
> Refer to Exercise 7.70. Find the quartiles of the time to complete the research project. Data from Exercise 7.70: A professor of business statistics is about to begin work on a new research project. Because his time is quite limited, he has developed a
> Refer to Exercise 7.69. Find the probability of the following events. a. The launch of the new product takes more than 105 days. b. The launch of the new product takes more than 92 days. c. The launch of the new product takes between 95 and 112 days. Da
> The mean and variance of the time to complete the project in Exercise 7.68 was 145 minutes and 31 minutes2. What is the probability that it will take less than 2.5 hours to overhaul the machine? Data from Exercise 7.68: The operations manager of a large
> Refer to Exercise 8.9. The operations manager labels any week that is in the bottom 20% of production a “bad week.” How many metric tons should be used to define a bad week? Data from Exercise 8.9: The weekly output of a steel mill is a uniformly distri
> In a survey of consumer finances, it was determined that the average household debt is $250,000. If household debt is normally distributed with a standard deviation of $30,000 determine the quintiles.
> The annual rate of return on a mutual fund is normally distributed with a mean of 14% and a standard deviation of 18%. a. What is the probability that the fund returns more than 25% next year? b. What is the probability that the fund loses money next yea
> Refer to Exercise 8.71. Any marble ryes that are unsold at the end of the day are marked down and sold for half-price. How many loaves should the bakery prepare so that the proportion of days that result in unsold loaves is no more than 60%? Data from E
> Every day a bakery prepares its famous marble rye. A statistically savvy customer determined that daily demand is normally distributed with a mean of 850 and a standard deviation of 90. How many loaves should the bakery make if it wants the probability o
> The average North American loses an average of 15 days per year to colds and flu. The natural remedy echinacea reputedly boosts the immune system. One manufacturer of echinacea pills claims that consumers of its product will reduce the number of days los
> Define relative efficiency.
> A professor of statistics noticed that the marks in his course are normally distributed. He has also noticed that his morning classes average 73%, with a standard deviation of 12% on their final exams. His afternoon classes average 77%, with a standard d
> A factory’s worker productivity is normally distributed. One worker produces an average of 75 units per day with a standard deviation of 20. Another worker produces at an average rate of 65 per day with a standard deviation of 21. What is the probability
> Repeat Exercise 9.64 assuming that the standard deviations are 12 and 16, respectively. Data from Exercise 9.64: Suppose that we have two normal populations with the means and standard deviations listed here. If random samples of size 25 are drawn from
> Suppose that we have two normal populations with the means and standard deviations listed here. If random samples of size 25 are drawn from each population, what is the probability that the mean of sample 1 is greater than the mean of sample 2? Populatio
> The operations manager of a plant making cellular telephones has proposed rearranging the production process to be more efficient. She wants to estimate the time to assemble the telephone using the new arrangement. She believes that the population standa
> The label on 1-gallon cans of paint states that the amount of paint in the can is sufficient to paint 400 square feet. However, this number is quite variable. In fact, the amount of coverage is known to be approximately normally distributed with a standa
> A medical researcher wants to investigate the amount of time it takes for patients’ headache to be relieved after taking a new prescription painkiller. She plans to use statistical methods to estimate the mean of the population of relief times. She belie
> Draw diagrams representing what happens to the sampling distribution of a consistent estimator when the sample size increases.
> A statistics professor wants to compare today’s students with those 25 years ago. All his current students’ marks are stored on a computer so that he can easily determine the population mean. However, the marks 25 years ago reside only in his musty files
> The operations manager of a large production plant would like to estimate the average amount of time workers take to assemble a new electronic component. After observing a number of workers assembling similar devices, she guesses that the standard deviat
> A medical statistician wants to estimate the average weight loss of people who are on a new diet plan. In a preliminary study, he guesses that the standard deviation of the population of weight losses is about 10 pounds. How large a sample should he take
> a. Repeat part (b) of Exercise 10.54 after discovering that the population standard deviation is actually 100. b. Repeat part (b) of Exercise 10.48 after discovering that the population standard deviation is actually 400.
> a. A statistics practitioner would like to estimate a population mean to within 10 units. The confidence level has been set at 95% and = 200. Determine the sample size. b. Suppose that the sample mean was calculated as 500. Estimate the population mean
> Review Exercises 10.51 and 10.52. Describe what happens to the confidence interval estimate when a. the standard deviation is equal to the value used to determine the sample size. b. the standard deviation is smaller than the one used to determine the sa
> a. Repeat part (b) in Exercise 10.51 after discovering that the population standard deviation is actually 5. b. Repeat part (b) in Exercise 10.45 after discovering that the population standard deviation is actually 20. Data from Exercise 10.51: a. Deter
> a. Determine the sample size necessary to estimate a population mean to within 1 with 90% confidence given that the population standard deviation is 10. b. Suppose that the sample mean was calculated as 150. Estimate the population mean with 90% confiden
> Review the results of Exercise 10.49. Describe what happens to the sample size when a. the population standard deviation decreases. b. the confidence level decreases. c. the bound on the error of estimation decreases.
> Define consistency.
> a. A statistics practitioner would like to estimate a population mean to within 50 units with 99% confidence given that the population standard deviation is 250. What sample size should be used? b. Re-do part (a) changing the standard deviation to 50. c.
> Review Exercise 10.47. Describe what happens to the sample size when a. the population standard deviation increases. b. the confidence level increases. c. the bound on the error of estimation increases.
> a. Determine the sample size required to estimate a population mean to within 10 units given that the population standard deviation is 50. A confidence level of 90% is judged to be appropriate. b. Repeat part (a) changing the standard deviation to 100. c
> The sponsors of television shows targeted at the children’s market wanted to know the amount of time children spend watching television because the types and number of programs and commercials are greatly influenced by this information. As a result, it w
> Registered Retirement Savings Plan are retirement plans that defer taxes. Many Canadians rely on these plans for their retirement. To measure how these are doing, a random sample of 60-yearold Canadians was drawn and asked to report the total value of th
> How much do American families spend on entertainment each month. A survey was conducted and the amounts spent on entertainment in the previous month were recorded. Assuming that the population standard deviation is $50 determine the 99% confidence interv
> The rising cost of electricity is a concern for homeowners. An economist wanted to determine how much electricity has increased over the past 5 years. A survey was conducted with the percentage increase recorded. Assuming that the population standard dev
> A survey of 80 randomly selected companies asked them to report the annual income of their presidents. Assuming that incomes are normally distributed with a standard deviation of $30,000, determine the 90% confidence interval estimate of the mean annual
> One measure of physical fitness is the amount of time it takes for the pulse rate to return to normal after exercise. A random sample of 100 women age 40 to 50 exercised on stationary bicycles for 30 minutes. The amount of time it took for their pulse ra
> The image of the Japanese manager is that of a workaholic with little or no leisure time. In a survey, a random sample of 250 Japanese middle managers was asked how many hours per week they spent in leisure activities (e.g., sports, movies, television).
> Draw a sampling distribution of a biased estimator.
> A time study of a large production facility was undertaken to determine the mean time required to assemble a cell phone. A random sample of the times to assemble 50 cell phones was recorded. An analysis of the assembly times reveals that they are normall
> As part of a project to develop better lawn fertilizers, a research chemist wanted to determine the mean weekly growth rate of Kentucky bluegrass, a common type of grass. A sample of 250 blades of grass was measured, and the amount of growth in 1 week wa
> A statistics professor is in the process of investigating how many classes university students miss each semester. To help answer this question, she took a random sample of 100 university students and asked each to report how many classes he or she had m
> In an article about disinflation, various investments were examined. The investments included stocks, bonds, and real estate. Suppose that a random sample of 200 rates of return on real estate investments was computed and recorded. Assuming that the stan
> In a survey conducted to determine, among other things, the cost of vacations, 64 individuals were randomly sampled. Each person was asked to compute the cost of her or his most recent vacation. Assuming that the standard deviation is $400, estimate with
> A survey of 400 statistics professors was undertaken. Each professor was asked how much time was devoted to teaching graphical techniques. We believe that the times are normally distributed with a standard deviation of 30 minutes. Estimate the population
> Because of different sales ability, experience, and devotion, the incomes of real estate agents vary considerably. Suppose that in a large city the annual income is normally distributed with a standard deviation of $15,000. A random sample of 16 real est
> One of the few negative side effects of quitting smoking is weight gain. Suppose that the weight gain in the 12 months following a cessation in smoking is normally distributed with a standard deviation of 6 pounds. To estimate the mean weight gain, a ran
> Suppose that the amount of time teenagers spend weekly working at part-time jobs is normally distributed with a standard deviation of 40 minutes. A random sample of 15 teenagers was drawn, and each reported the amount of time spent at part-time jobs (in
> It is known that the amount of time needed to change the oil on a car is normally distributed with a standard deviation of 5 minutes. The amount of time to complete a random sample of 10 oil changes was recorded and listed here. Compute the 99% confidenc
> Draw a sampling distribution of an unbiased estimator.
> The number of cars sold annually by used car salespeople is normally distributed with a standard deviation of 15. A random sample of 15 salespeople was taken, and the number of cars each sold is listed here. Find the 95% confidence interval estimate of t
> Among the most exciting aspects of a university professor’s life are the departmental meetings where such critical issues as the color of the walls will be painted and who gets a new desk are decided. A sample of 20 professors was asked
> How many rounds of golf do physicians (who play golf) play per year? A survey of 12 physicians revealed the following numbers: 3 41 17 1 33 37 18 15 17 12 29 51 Estimate with 95% confidence the mean number of rounds per year played by physicians, assumin
> The following observations are the ages of a random sample of 8 men in a bar. It is known that the ages are normally distributed with a standard deviation of 10. Determine the 95% confidence interval estimate of the population mean. Interpret the interva
> The following data represent a random sample of 9 marks (out of 10) on a statistics quiz. The marks are normally distributed with a standard deviation of 2. Estimate the population mean with 90% confidence. 7 9 7 5 4 8 3 10 9
> a. Given the following information, determine the 90% confidence interval estimate of the population mean using the sample median. Sample median = 500, = 12, and n = 50 b. Compare your answer in part (a) to that produced in part (c) of Exercise 10.16.
> Show that the sample mean is relatively more efficient than the sample median when estimating the population mean.
> Is the sample median a consistent estimator of the population mean? Explain.
> Is the sample median an unbiased estimator of the population mean? Explain.
> a. A random sample of 100 observations was randomly drawn from a population with a standard deviation of 5. The sample mean was calculated as x = 400. Estimate the population mean with 99% confidence. b. Repeat part (a) with x = 200. c. Repeat part (a) w
> Define unbiasedness.
> a. From the information given here determine the 95% confidence interval estimate of the population mean. x = 100 = 20 n = 25 b. Repeat part (a) with x = 200. c. Repeat part (a) with x = 500. d. Describe what happens to the width of the confidence inte
> a. A statistics practitioner randomly sampled 100 observations from a population with a standard deviation of 5 and found that x is 10. Estimate the population mean with 90% confidence. b. Repeat part (a) with a sample size of 25. c. Repeat part (a) with
> a. The mean of a sample of 25 was calculated as x = 500. The sample was randomly drawn from a population with a standard deviation of 15. Estimate the population mean with 99% confidence. b. Repeat part (a) changing the population standard deviation to 3
> a. Given the following information, determine the 98% confidence interval estimate of the population mean: x = 500 = 12 n = 50 b. Repeat part (a) using a 95% confidence level. c. Repeat part (a) using a 90% confidence level. d. Review parts (a)–(c) and
> a. A random sample of 25 was drawn from a normal distribution with a standard deviation of 5. The sample mean is 80. Determine the 95% confidence interval estimate of the population mean. b. Repeat part (a) with a sample size of 100. c. Repeat part (a) w
> a. The mean of a random sample of 25 observations from a normal population with a standard deviation of 50 is 200. Estimate the population mean with 95% confidence. b. Repeat part (a) changing the population standard deviation to 25. c. Repeat part (a) c
> a. A statistics practitioner took a random sample of 50 observations from a population with a standard deviation of 25 and computed the sample mean to be 100. Estimate the population mean with 90% confidence. b. Repeat part (a) using a 95% confidence lev
> Refer to Exercises 9.9–9.11. What do the probabilities tell you about the variances of X and X? Data from Exercise 9.9: Let X represent the result of the toss of a fair die. Find the following probabilities. Data from Exercise 9.11: An experiment consi
> An experiment consists of tossing five balanced dice. Find the following probabilities. (Determine the exact probabilities as we did in Tables 9.1 and 9.2 for two dice.) a. P(X = 1) b. P(X = 6) Data from Table 9.1: Data from Table 9.2: TABLE 9.1 Al
> Let X represent the mean of the toss of two fair dice. Use the probabilities listed in Table 9.2 to determine the following probabilities. a. P(X = 1) b. P(X = 6) Data from Table 9.2: TABLE 9.2 Sampling Distribution of X P(X) 1.0 1/36 1.5 2/36 2.0 3
> How do point estimators and interval estimators differ?
