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Statistics The Exploration And Analysis Of Data 6th Edition John M Scheb, Jay Devore, Roxy Peck - Solutions

=+8.30 Suppose that a particular candidate for public office is in fact favored by 48% of all registered voters in the district. A polling organization will take a random sample of 500 voters and will use p, the sample proportion, to estimate p. What is the approximate probability that p will be
=+c. Without doing any calculations, how do you think the probabilities in Part (b) would change if n were 400 rather than 225?
=+b. Calculate P(p $ .6) for both p 5 .5 and p 5 .6.
=+a. If p 5 .5, what are the mean value and standard deviation of p? Answer this question for p 5 .6. Does p have approximately a normal distribution in both cases? Explain.
=+p denote the actual proportion of college graduates who are avid readers of mystery novels. Consider a sample proportion p that is based on a random sample of 225 college graduates.
=+8.29 The article “Thrillers” (Newsweek, April 22, 1985)stated, “Surveys tell us that more than half of America’s college graduates are avid readers of mystery novels.” Let
=+d. Is the probability calculated in Part (c) larger or smaller than would be the case if n 5 500? Answer without actually calculating this probability.
=+c. When n 5 400, what is P(.25 # p # .35)?
=+b. What are the mean value and standard deviation of p based on a random sample of size 400?
=+a. Would p based on a random sample of only 10 residents have approximately a normal distribution? Explain why or why not.
=+York residents who live within 1 mi of such a site, and suppose that p 5 .3.
=+8.28 The article “Should Pregnant Women Move? Linking Risks for Birth Defects with Proximity to Toxic Waste Sites” (Chance [1992]: 40–45) reported that in a large study carried out in the state of New York, approximately 30% of the study subjects lived within 1 mi of a hazardous waste
=+c. What is the smallest value of n for which the sampling distribution of p is approximately normal?
=+b. Does p have approximately a normal distribution in this case? Explain.
=+what is the standard deviation of the sample proportion?
=+a. What is the mean value of the sample proportion p, and
=+8.27 ▼ A certain chromosome defect occurs in only 1 out of 200 adult Caucasian males. A random sample of n 5 100 adult Caucasian males is to be obtained.
=+8.26 The article referenced in Exercise 8.25 reported that for unmarried couples living together, the proportion that are racially or ethnically mixed is .15. Answer the questions posed in Parts (a)–(e) of Exercise 8.25 for the population of unmarried couples living together.
=+e. When n 5 200, what is the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than .10?
=+d. Is it reasonable to assume that the sampling distribution of p is approximately normal for random samples of size n 5 200? Explain.
=+c. Suppose that the sample size is n 5 200 rather than n 5 100, as in Part (b). Does the change in sample size change the mean and standard deviation of the sampling distribution of p? If so, what are the new values for the mean and standard deviation? If not, explain why not.
=+b. Is it reasonable to assume that the sampling distribution of p is approximately normal for random samples of size n 5 100? Explain.
=+a. A random sample of n 5 100 couples will be selected from this population and p, the proportion of couples that are mixed racially or ethnically, will be computed. What are the mean and standard deviation of the sampling distribution of p?
=+8.25 ▼ The article “Unmarried Couples More Likely to Be Interracial” (San Luis Obispo Tribune, March 13, 2002)reported that 7% of married couples in the United States are mixed racially or ethnically. Consider the population consisting of all married couples in the United States.
=+8.24 For which of the sample sizes given in Exercise 8.23 would the sampling distribution of p be approximately normal if p 5 .65? if p 5 .2?
=+8.23 A random sample is to be selected from a population that has a proportion of successes p 5 .65. Determine the mean and standard deviation of the sampling distribution of p for each of the following sample sizes:a. n 5 10d. n 5 50b. n 5 20e. n 5 100c. n 5 30f. n 5 200
=+d. Suppose that a machine used to apply the coating is out of adjustment, resulting in a mean coating thickness of 3.05 mm. What is the probability that a problem will be detected when the next sample is taken? (Hint: This will occur if m 5.
=+c. Referring to Part (b), what is the probability that a sample mean will be outside just by chance (i.e., when there are no unusual circumstances)?
=+b. When no unusual circumstances are present, we expect to be within of 3 mm, the desired value. An value farther from 3 than is interpreted as an indication of a problem that needs attention. Compute . (A plot over time of values with horizontal lines drawn at the limits is called a process
=+a. Describe the sampling distribution of (for a sample of size 16).
=+8.22 The thickness (in millimeters) of the coating applied to disk drives is a characteristic that determines the usefulness of the product. When no unusual circumstances are present, the thickness (x) has a normal distribution with a mean of 3 mm and a standard deviation of 0.05 mm. Suppose
=+dard deviation of 20 lb. If 100 passengers will board a flight, what is the approximate probability that the total weight of their baggage will exceed the limit? (Hint: With n 5 100, the total weight exceeds the limit when the average weight exceeds 6000/100.)
=+8.21 ▼ An airplane with room for 100 passengers has a total baggage limit of 6000 lb. Suppose that the total weight of the baggage checked by an individual passenger is a random variable x with a mean value of 50 lb and a stanx xx xx
=+c. Referring to Part (b), what is the approximate probability that is at most 20? at least 25?
=+b. Suppose that the mean value of x is 22.0 and that the standard deviation is 16.5. If a random sample of n 5 100 customers is to be selected and denotes the sample average number of checks written during a particular month, where is the sampling distribution of centered, and what is the
=+a. Give a sketch of what the probability distribution of x might look like.
=+8.20 College students with a checking account typically write relatively few checks in any given month, whereas nonstudent residents typically write many more checks during a month. Suppose that 50% of a bank’s accounts are held by students and that 50% are held by nonstudent residents. Let x
=+greater than 0.51 in., the process is shut down for adjustment. The standard deviation for diameter is 0.02 in. What is the probability that the manufacturing line will be shut down unnecessarily? (Hint: Find the probability of observing an in the shutdown range when the true process mean
=+sample of 36 bolts is selected and the diameters recorded.If the resulting sample mean is less than 0.49 in. or
=+8.19 A manufacturing process is designed to produce bolts with a 0.5-in. diameter. Once each day, a random
=+ii. Approximately 0.3% of the time, will be farther than _____ from m.
=+i. Approximately 95% of the time, will be within _____ of m.
=+b. For this example (n 5 100, s 5 10), complete each of the following statements by computing the appropriate value:
=+a. What is the probability that the sample mean will be within 2 of the value of m?
=+8.18 Suppose that a sample of size 100 is to be drawn from a population with standard deviation 10.
=+b. Suppose that a sample of 100 adult males is to be obtained. Without assuming that interpupillary distance is normally distributed, what is the approximate probability that the sample average distance will be between 64 and 67 mm? at least 68 mm?
=+a. If the distribution of interpupillary distance is normal and a sample of n 5 25 adult males is to be selected, what is the probability that the sample average distance for these 25 will be between 64 and 67 mm? at least 68 mm?
=+8.17 Suppose that the mean value of interpupillary distance (the distance between the pupils of the left and right eyes) for adult males is 65 mm and that the population standard deviation is 5 mm.
=+d. What is the chance that a random sample of 16 persons on the elevator will exceed the weight limit?
=+c. What average weights for a sample of 16 people will result in the total weight exceeding the weight limit of 2500 lb?
=+b. What is the standard deviation of the sampling distribution of the sample mean weight?
=+a. What is the mean value of the distribution of the sample mean?
=+8.16 In the library on a university campus, there is a sign in the elevator that indicates a limit of 16 persons.Furthermore, there is a weight limit of 2500 lb. Assume that the average weight of students, faculty, and staff on campus is 150 lb, that the standard deviation is 27 lb, and that the
=+b. Repeat Part (a) for a sample of size of n 5 20 and again for a sample of size n 5 100. How do the centers and spreads of the three distributions compare to one another? Which sample size would be most likely to result in an value close to x m, and why?x xx xx xx xx xmx sx x
=+a. If is the sample average time for a random sample of n 5 9 students, where is the distribution centered, and how much does it spread out about the center (as described by its standard deviation)?
=+8.15 Let x denote the time (in minutes) that it takes a fifth-grade student to read a certain passage. Suppose that the mean value and standard deviation of x are m 5 2 min and s 5 0.8 min, respectively.
=+b. Answer Part (a) for a random sample of 50 individuals.In this case, sketch a picture of a good approximation to the actual distribution.
=+a. Let be the sample average waiting time for a random sample of 16 individuals. What are the mean and standard deviation of the sampling distribution of ?
=+8.14 The time that a randomly selected individual waits for an elevator in an office building has a uniform distribution over the interval from 0 to 1 min. It can be shown that for this distribution m 5 0.5 and s 5 0.289.
=+c. What is the approximate probability that will differ from m by more than 0.7?
=+b. What is the approximate probability that will be within 0.5 of the population mean m?
=+a. What are the mean and standard deviation of the sampling distribution? Describe the shape of the sampling distribution.
=+8.13 ▼ Suppose that a random sample of size 64 is to be selected from a population with mean 40 and standard deviation 5.
=+8.12 Explain the difference between s and and between m and .
=+8.11 For which of the sample sizes given in Exercise 8.10 would it be reasonable to think that the sampling distribution is approximately normal in shape?
=+8.10 A random sample is selected from a population with mean m 5 100 and standard deviation s 5 10. Determine the mean and standard deviation of the sampling distribution for each of the following sample sizes:a. n 5 9d. n 5 50b. n 5 15e. n 5 100c. n 5 36f. n 5 400
=+3. Construct the sampling distribution of each of these statistics. Which statistic would you recommend for estimating m and why
=+A random sample of size 3 will be selected without replacement. Provided that we disregard the order in which the observations are selected, there are 10 possible samples that might result (writing 3 and 3*, 4 and 4* to distinguish the two 3’s and the two 4’s in the population):2, 3, 3* 2,
=+8.9 Consider the following population: {2, 3, 3, 4, 4}.The value of m is 3.2, but suppose that this is not known to an investigator, who therefore wants to estimate m from sample data. Three possible statistics for estimating m are Statistic 1: the sample mean, Statistic 2: the sample median
=+8.7 by using four slips of paper individually marked 1, 2, 3, and 4. Select a sample of size 2 without replacement, and compute . Repeat this process 50 times, and construct a density histogram of the 50 values. How does this sampling distribution compare to the sampling distribution of derived
=+8.8 Simulate sampling from the population of Exercise
=+c. In what ways are the two sampling distributions of Parts (a) and (b) similar? In what ways are they different?
=+b. Suppose that a random sample of size 2 is to be selected, but this time sampling will be done with replacement. Using a method similar to that of Part (a), construct the sampling distribution of . (Hint: There are 16 different possible samples in this case.)
=+Compute the sample mean for each of the 12 possible samples. Use this information to construct the sampling m 5 1 1 2 1 3 1 4 45 2.5 xx xx xx distribution of . (Display the sampling distribution as a density histogram.)
=+a. Suppose that a random sample of size 2 is to be selected without replacement from this population. There are 12 possible samples (provided that the order in which observations are selected is taken into account):1, 2 1, 3 1, 4 2, 1 2, 3 2, 4 3, 1 3, 2 3, 4 4, 1 4, 2 4, 3
=+8.7 ▼ Consider the following population: {1, 2, 3, 4}.Note that the population mean is
=+5. If 50 samples of size 10 were selected, the value for each sample computed, and a density histogram constructed, how do you think this histogram would differ from the density histogram constructed for samples of size 5 (Figure 8.1)? In what way would it be similar?
=+8.6 Suppose that the sampling experiment described in Example 8.1 had used samples of size 10 rather than size
=+8.5 Select 10 additional random samples of size 5 from the population of 20 students given in Example 8.1, and compute the mean amount spent on books for each of the 10 samples. Are the values consistent with the results of the sampling experiment summarized in Figure 8.1?
=+Do the values differ a lot from sample to sample, or do they tend to be similar?
=+d. Construct a density histogram using the 25 values.Are most of the values near the population mean?
=+c. Repeatedly select samples of size 2, and compute the value for each sample until you have the results of 25 samples.
=+b. Select a random sample of size 2 by writing the numbers on slips of paper, mixing them, and then selecting 2.Compute the mean of your sample.
=+a. Compute the mean of this population.
=+8.4 Consider a population consisting of the following five values, which represent the number of video rentals during the academic year for each of five housemates:8 14 16 10 11
=+e. A consumer group, after testing 100 batteries of a certain brand, reported an average life of 63 hr of use.
=+d. A hospital reports that based on the 10 most recent cases, the mean length of stay for surgical patients is 6.4 days.
=+c. The Department of Motor Vehicles reports that 22%of all vehicles registered in a particular state are imports.
=+b. A sample of 100 students at a large university had a mean age of 24.1 years.x
=+a. A department store reports that 84% of all customers who use the store’s credit plan pay their bills on time.
=+8.3 ▼ For each of the following statements, identify the number that appears in boldface type as the value of either a population characteristic or a statistic:
=+8.2 What is the difference between and m? between s and s?
=+8.1 Explain the difference between a population characteristic and a statistic.
=+c. Calculate P(x , 95 or x . 145), the probability that x is more than 2.5 standard deviations from its mean value.
=+a. Calculate P(110 , x , 140). How does this compare to P(110 # x # 140), and why?b. Calculate P(x , 75).
=+a large study in which a sample histogram of blood pressures among women of similar ages was found to be well approximated by a normal curve.)
=+120 mm Hg and standard deviation s 5 10 mm Hg is a reasonable model for describing the population distribution of x. (The article “Oral Contraceptives, Pregnancy, and Blood Pressure,” Journal of the American Medical Association [1972]: 1507–1510, reported on the results of
=+7.52 Let x denote the systolic blood pressure of an individual selected at random from a certain population.Suppose that the normal distribution with mean m 5
=+e. Some insurance companies will pay the medical expenses associated with childbirth only if the insurance has been in effect for more than 9 months (275 days). This restriction is designed to ensure that the insurance company has to pay benefits only for those pregnancies for which conception
=+d. A Dear Abby column dated January 20, 1973, contained a letter from a woman who stated that the duration of her pregnancy was exactly 310 days. (She wrote that the last visit with her husband, who was in the navy, occurred 310 days before the birth.) What is the probability that the duration

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