Refer to Exercise 8.44. If we wanted to be sure that 98% of all bulbs last longer than the advertised figure, what figure should be advertised? Data from Exercise 8.44: The lifetimes of lightbulbs that are advertised to last for 5,000 hours are normally distributed with a mean of 5,100 hours and a standard deviation of 200 hours. What is the probability that a bulb lasts longer than the advertised figure?
> Redo the SSA example with a. σ = 3 b. σ = 12 c. Discuss the effect on the test statistic and the p-value when σ increases.
> Redo the SSA example with a. σ = 3 b. σ = 12 c. Discuss the effect on the test statistic and the p-value when σ increases.
> You are the centerfielder of the New York Yankees. It is the bottom of the ninth inning of the seventh game of the World Series. The Yanks lead by 2 with 2 outs and men on second and third. The batter is known to hit for high average and runs very well b
> While conducting a test to determine whether a population mean is less than 900, you find that the sample mean is 1,050. a. Can you make a decision on this information alone? Explain. b. If you did calculate the p-value, would it be smaller or larger tha
> Redo Example 11.1 with a. σ = 35 b. σ = 100 c. Describe the effect on the test statistic and the p-value when σ increases. Data from Example 11.1: FIGURE 11.1 Sampling Distribution for Example 11.1 A-170 Rejection re
> Redo Example 11.1 with a. n = 200 b. n = 100 c. Describe the effect on the test statistic and the p-value when n increases. Data from Example 11.1: FIGURE 11.1 Sampling Distribution for Example 11.1 A-170 Rejection region
> a. Calculate the p-value of the test described here. H0: μ = 60 H1: μ > 60 x = 72, n = 25, σ = 20 b. Repeat part (a) with x = 68. c. Repeat part (a) with x = 64. d. Describe the effect on the test statistic and the p-value of the test when the value of x
> a. Find the p-value of the following test given that x = 990, n = 100, and σ = 25. H0: μ = 1000 H1: μ < 1000 b. Repeat part (a) with σ = 50. c. Repeat part (a) with σ = 100. d. Describe what happens to the value of the test statistic and its p-value when
> a. Test these hypotheses by calculating the p-value given that x = 99, n = 100, and σ = 8. H0: μ = 100 H1: μ ≠ 100 b. Repeat part (a) with n = 50. c. Repeat part (a) with n = 20. d. What is the effect on the value of the test statistic and the p-value of
> a. Given the following hypotheses, determine the p-value when x = 21, n = 25, and σ = 5. H0: μ = 20 H1: μ ≠ 20 b. Repeat part (a) with x = 22. c. Repeat part (a) with x = 23. d. Describe what happens to the value of the test statistic and its p-value whe
> a. A statistics practitioner formulated the following hypotheses H0: μ = 200 H1: μ < 200 and learned that x = 190, n = 9, and σ = 50 Compute the p-value of the test. b. Repeat part (a) with σ = 30. c. Repeat part (a) with σ = 10. d. Discuss what happens
> You are conducting a test to determine whether there is enough statistical evidence to infer that a population mean is greater than 100. You discover that the sample mean is 95. a. Is it necessary to do any further calculations? Explain. b. If you did ca
> 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 not equal to –5. σ = 5, n = 25, x = − 4.0
> 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 not equal to 0. σ = 50, n = 90, x = − 5.5.
> Repeat Exercise 9.15 with n = 25. Data from Exercise 9.15: A sample of n = 16 observations is drawn from a normal population with μ = 1,000 and σ = 200. Find the following. a. P(X > 1,050) b. P(X < 960) c. P(X > 1,100)
> 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 0. σ = 25, n = 400, x = − 2.3
> A sample of n = 16 observations is drawn from a normal population with μ = 1,000 and σ = 200. Find the following. a. P(X > 1,050) b. P(X < 960) c. P(X > 1,100)
> Refer to Exercise 9.13. Suppose that the population is not normally distributed. Does this change your answer? Explain. Data from Exercise 9.13: A normally distributed population has a mean of 40 and a standard deviation of 12. What does the central lim
> A normally distributed population has a mean of 40 and a standard deviation of 12. What does the central limit theorem say about the sampling distribution of the mean if samples of size 100 are drawn from this population?
> Refer to Example 3.2. From the histogram for investment A, estimate the following probabilities. a. P(X > 45) b. P(10 c. P(X d. P(35 Data from Example 3.2: Histogram of Returns on InvestmentA 18 16 2 -30 -15 15 30 45 60 76 Returns kouenbay
> The weekly output of a steel mill is a uniformly distributed random variable that lies between 110 and 175 metric tons. a. Compute the probability that the steel mill will produce more than 150 metric tons next week. b. Determine the probability that the
> The demand for a daily newspaper at a newsstand at a busy intersection is known to be normally distributed with a mean of 150 and a standard deviation of 25. How many newspapers should the newsstand operator order to ensure that he runs short on no more
> A retailer of computing products sells a variety of computer-related products. One of his most popular products is an HP laser printer. The average weekly demand is 200. Lead time for a new order from the manufacturer to arrive is 1 week. If the demand f
> According to the Statistical Abstract of the United States, 2012 (Table 721), the mean family net worth of families whose head is between 35 and 44 years old is approximately $325,600. If family net worth is normally distributed with a standard deviation
> The daily withdrawals from an ATM located at a service station is normally distributed with a mean of $50,000 and a standard deviation of $8,000. The operator of the ATM puts $64,000 in cash at the beginning of the day. What is the probability that the A
> Mensa is an organization whose members possess IQs that are in the top 2% of the population. It is known that IQs are normally distributed with a mean of 100 and a standard deviation of 16. Find the minimum IQ needed to be a Mensa member.
> 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 greater than 0. σ = 10, n = 100, x = 1.5
> The final marks in a statistics course are normally distributed with a mean of 70 and a standard deviation of 10. The professor must convert all marks to letter grades. She decides that she wants 10%A’s, 30%B’s, 40%C’s, 15%D’s, and 5%F’s. Determine the c
> How much money does a typical family of four spend at a McDonald’s restaurant per visit? The amount is a normally distributed random variable with a mean of $16.40 and a standard deviation of $2.75. a. Find the probability that a family of four spends le
> It is said that sufferers of a cold virus experience symptoms for 7 days. However, the amount of time is actually a normally distributed random variable whose mean is 7.5 days and whose standard deviation is 1.2 days. a. What proportion of cold sufferers
> Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid monthly by a bank’s Visa cardholders reveals that the amou
> Battery manufacturers compete on the basis of the amount of time their products last in cameras and toys. A manufacturer of alkaline batteries has observed that its batteries last for an average of 26 hours when used in a toy racing car. The amount of ti
> A golfer playing a new course encounters a hole that requires a drive of 145 yards to successfully clear a pond. She knows that her drives are normally distributed with a mean of 155 yards and a standard deviation of 9 yards. What is the probability that
> The mean monthly income of graduates of professional and Ph.D. degrees is $6,000 according to a recent PEW Research Center survey. If these incomes are normally distributed with a standard deviation of $1,200, a. What proportion of incomes is greater tha
> Refer to Exercise 8.57. The manufacturer wants to provide guidelines to potential customers advising them of the minimum number of pages they can expect from each cartridge. How many pages should it advertise if the company wants to be correct 99% of the
> The number of pages printed before replacing the cartridge in a laser printer is normally distributed with a mean of 11,500 pages and a standard deviation of 800 pages. A new cartridge has just been installed. a. What is the probability that the printer
> The amount of time devoted to studying statistics each week by students who achieve a grade of A in the course is a normally distributed random variable with a mean of 7.5 hours and a standard deviation of 2.1 hours. a. What proportion of A student’s stu
> 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 greater than 7.5. σ = 1.5, n = 30, x = 8.5
> Refer to Exercise 8.54. Find the amount of sleep that is exceeded by only 25% of students. Data from Exercise 8.54: University and college students average 7.2 hours of sleep per night, with a standard deviation of 40 minutes. If the amount of sleep is
> University and college students average 7.2 hours of sleep per night, with a standard deviation of 40 minutes. If the amount of sleep is normally distributed, what proportion of university and college students sleep for more than 8 hours?
> Refer to Exercise 8.52. Find the probability of these events. a. A 2-year-old child is taller than 36 inches. b. A 2-year-old child is shorter than 34 inches. c. A 2-year-old child is between 30 and 33 inches tall. Data from Exercise 8.52: The heights o
> The heights of 2-year-old children are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches. Pediatricians regularly measure the heights of toddlers to determine whether there is a problem. There may be a problem when a ch
> The top-selling Red and Voss tire is rated 70,000 miles, which means nothing. In fact, the distance the tires can run until they wear out is a normally distributed random variable with a mean of 82,000 miles and a standard deviation of 6,400 miles. a. Wh
> Economists frequently make use of quintiles (i.e., the 20th, 40th, 60th, and 80th percentiles) particularly when discussing incomes. Suppose that in a large city household income are normally distributed with a mean of $50,000 and a standard deviation of
> Exercise 4.67 addressed the problem of setting an appropriate speed limit on highways. Automotive experts believe that the “correct” speed is the 85th percentile. Suppose that the speeds on a highway are normally distributed with a mean of 68 and a stand
> The Tesla Model S 85D is an electric car that the manufacturer claims can travel 270 miles on a single charge. However, the actual distance depends on a number of factors including speed and whether the car is driven in the city or on highways. Suppose t
> According to a PEW Research Center survey, the mean student loan at graduation is $25,000. Suppose that student loans are normally distributed with a standard deviation of $5,000. A graduate with a student loan is selected at random. Find the following p
> SAT scores are normally distributed with a mean of 1,000 and a standard deviation of 300. Find the quartiles.
> 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 not equal to 1,500. σ = 220, n = 125, x = 1525
> The lifetimes of lightbulbs that are advertised to last for 5,000 hours are normally distributed with a mean of 5,100 hours and a standard deviation of 200 hours. What is the probability that a bulb lasts longer than the advertised figure?
> Refer to Exercise 8.42. How long do the longest 10% of calls last? Data from Exercise 8.42: The long-distance calls made by the employees of a company are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.2 minutes. Find the
> The long-distance calls made by the employees of a company are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.2 minutes. Find the probability that a call a. lasts between 5 and 10 minutes. b. lasts more than 7 minutes. c. l
> 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
