MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Transcription

1 Ch. 9 Estimating the Value of a Parameter 9.1 Estimating a Population Proportion 1 Obtain a point estimate for the population proportion. 1) When 390 junior college students were surveyed,115 said that they have previously owned a motorcycle. Find a point estimate for p, the population proportion of students who have previously owned a motorcycle. A) B) C) D) ) A survey of 100 fatal accidents showed that in 24 cases the driver at fault was inadequately insured. Find a point estimate for p, the population proportion of accidents where the driver at fault was inadequately insured A) 0.24 B) 0.76 C) D) ) A survey of 400 non-fatal accidents showed that 173 involved faulty equipment. Find a point estimate for p, the population proportion of accidents that involved faulty equipment. A) B) C) D) ) A survey of 250 households showed 26 owned at least one snow blower. Find a point estimate for p, the population proportion of households that own at least one snow blower. A) B) C) D) ) A survey of 2390 musicians showed that 304 of them are left-handed. Find a point estimate for p, the population proportion of musicians that are left-handed. A) B) C) D) ) A marketing research company needs to estimate which of two medical plans its employees prefer. A random sample of n employees produced the following 90% confidence interval for the proportion of employees who prefer plan A: (0.347, 0.647). Identify the point estimate for estimating the true proportion of employees who prefer that plan. A) B) 0.15 C) D) ) Many people think that a national lobbyʹs successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4000 citizens yielded 2200 who are in favor of gun control legislation. Find the point estimate for estimating the proportion of all Americans who are in favor of gun control legislation. A) B) 2200 C) 4000 D) Construct and interpret a confidence interval for the population proportion. Determine the critical value zα/2 that corresponds to the given level of confidence. 8) 90% A) B) 1.28 C) 0.82 D) ) 97% A) 2.17 B) 1.88 C) 0.83 D) 1.92 Page 1

2 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 10) When 415 junior college students were surveyed, 150 said they have a passport. Construct a 95% confidence interval for the proportion of junior college students that have a passport. Round to the nearest thousandth. 11) A survey of 700 non-fatal accidents showed that 167 involved uninsured drivers. Construct a 99% confidence interval for the proportion of fatal accidents that involved uninsured drivers. Round to the nearest thousandth. 12) In a survey of 10 musicians, 2 were found to be left-handed. Is it practical to construct the 90% confidence interval for the population proportion, p? Explain. 13) An article a Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the familyʹs financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 522 teenagers. Estimate the proportion of all teenagers who want more family discussions about school. Use a 99% confidence level. Express the answer in the form p^ ± E and round to the nearest thousandth. A) 0.37 ± B) 0.37 ± C) 0.63 ± D) 0.63 ± ) Many people think that a national lobbyʹs successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4000 citizens yielded 2250 who are in favor of gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a 90% confidence interval. Express the answer in the form p^ ± E and round to the nearest ten-thousandth. A) ± B) ± C) ± D) ± ) A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. Use a 98% confidence interval to estimate the true proportion of students on financial aid. Express the answer in the form p^ ± E and round to the nearest thousandth. A) 0.59 ± B) 0.59 ± C) 0.59 ± D) 0.59 ± ) True or False: The general form of a large-sample (1 - α) 100% confidence interval for a population proportion p^(1 - p^) p is p^ ± z α/2, where p^ = x is the sample proportion of observations with the characteristic of n n interest. A) True B) False 17) What is the best point estimate for p in order to construct a confidence interval for p? A) p^ B) μp C) p D) p ~ 18) A confidence interval for p can be constructed using A) p^ ± zα/2 p^(1 - p^) n B) p ± z σ n C) p^ ± z σ n D) p ± zα/2 p(1 - p) n Page 2

3 3 Find the sample size needed for estimating a population proportion within a given margin of error. 19) A researcher at a major clinic wishes to estimate the proportion of the adult population of the United States that has sleep deprivation. How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 4%? A) 423 B) 11 C) 846 D) ) A senator wishes to estimate the proportion of United States voters who favor abolishing the Electoral College. How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 3%? A) 1509 B) 1068 C) 20 D) ) A private opinion poll is conducted for a politician to determine what proportion of the population favors adding more national parks. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4%? A) 601 B) 423 C) 1201 D) 13 22) A pollster wishes to estimate the number of left-handed scientists. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4%? A previous study indicates that the proportion of left-handed scientists is 8%. A) 177 B) 125 C) 193 D) 24 23) A researcher wishes to estimate the number of households with two computers. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 3%? A previous study indicates that the proportion of households with two computers is 20%. A) 1179 B) 966 C) 1474 D) 5 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 24) A state highway patrol official wishes to estimate the number of legally intoxicated drivers on a certain road. a) How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 2%? b) Repeat part (a) assuming previous studies found that 85% of the drivers on this road are legally intoxicated. 25) A local outdoor equipment store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will randomly sample among its 100,000 items in order to determine the proportion of merchandise that is outdated. The current owners have never determined their outdated percentage and can not help the buyers. Approximately how large a sample do the buyers need in order to insure that they are 98% confident that the margin of error is within 3%? A) 1509 B) 3017 C) 6033 D) ) A confidence interval was used to estimate the proportion of math majors that are female. A random sample of 72 math majors generated the following confidence interval: (0.438, 0.642). Using the information above, what size sample would be necessary if we wanted to estimate the true proportion to within 4% using 99% reliability? A) 1030 B) 1037 C) 1078 D) 995 Page 3

4 27) Many people think that a national lobbyʹs successful fight against gun control legislation is reflecting the will of a minority of Americans. A previous random sample of 4000 citizens yielded 2250 who are in favor of gun control legislation. How many citizens would need to be sampled if a 90% confidence interval was desired to estimate the true proportion to within 4%? A) 417 B) 440 C) 423 D) ) A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 4% with 90% reliability, how many students would need to be sampled? A) 410 B) 99 C) 249 D) 17 29) In a college student poll, it is of interest to estimate the proportion p of students in favor of changing from a quarter-system to a semester-system. How many students should be polled so that we can estimate p to within 0.09 using a 99% confidence interval? A) 205 B) 182 C) 261 D) ) True or False? When choosing the sample size for estimating a population proportion p to within E units with confidence (1 - α)100%, if you take p 0.5 as the approximation to p, you will always obtain a sample size that is at least as large as required. A) True B) False 31) True or False? If no estimate of p exists when determining the sample size, we can use 0.5 in the formula to get a value for n. A) True B) False 9.2 Estimating a Population Mean 1 Obtain a point estimate for the population mean. 1) Determine the point estimate of the population mean and margin of error for the confidence interval with lower bound 19 and upper bound: 27. A) x = 23, E = 4 B) x = 23, E = 8 C) x = 19, E = 8 D) x = 27, E = 4 Page 4

5 2 State properties of Studentʹs t-distribution. A simple random sample of size n < 30 for a quantitative variable has been obtained. Using the normal probability plot, the correlation between the variable and expected z -score, and the boxplot, judge whether a t -interval should be constructed. 2) n = 14; Correlation = A) Yes B) No Page 5

6 3) n = 10; Correlation = A) No B) Yes A simple random sample of size n < 30 has been obtained. From the boxplot, judge whether a t -interval should be constructed. 4) A) No, though there are no outliers, the data are not normally distributed but right skewed B) No, there are outliers and the data are not normally distributed but right skewed C) Yes; the data are normally distributed and there are no outliers D) No; the data are normally distributed, but there are outliers Page 6

7 5) A) No; the data appear roughly normally distributed but there are outliers B) Yes; the data appear normally distributed and there are no outliers C) No, there are outliers and the data are not normally distributed D) No, there are no outliers but the data are not normally distributed 6) A) Yes; the data appear roughly normally distributed and there are no outliers B) No; the data are not normally distributed and there are outliers C) No; there are no outliers, but the data are not normally distributed D) No; the data appear roughly normally distributed, but there are outliers 7) Suppose a 98% confidence interval for μ turns out to be (1000, 2100). If this interval was based on a sample of size n = 22, explain what assumptions are necessary for this interval to be valid. A) The population must have an approximately normal distribution. B) The sampling distribution of the sample mean must have a normal distribution. C) The population of salaries must have an approximate t distribution. D) The sampling distribution must be biased with 21 degrees of freedom. 8) A computer package was used to generate the following printout for estimating the sale price of condominiums in a particular neighborhood. X = sale_price SAMPLE MEAN OF X = 46,500 SAMPLE STANDARD DEV = 13,747 SAMPLE SIZE OF X = 15 CONFIDENCE = 99 UPPER LIMIT = 57, SAMPLE MEAN OF X = 46,500 LOWER LIMIT = 35, What assumptions are necessary for any inferences derived from this printout to be valid? A) The sample was randomly selected from an approximately normal population. B) The sample variance equals the population variance. C) The population mean has an approximate normal distribution. D) All of these are necessary. Page 7

8 9) A computer package was used to generate the following printout for estimating the sale price of condominiums in a particular neighborhood. X = sale_price SAMPLE MEAN OF X = 46,500 SAMPLE STANDARD DEV = 13,747 SAMPLE SIZE OF X = 15 CONFIDENCE = 98 UPPER LIMIT = 55, SAMPLE MEAN OF X = 46,500 LOWER LIMIT = 37, A friend suggests that the mean sale price of homes in this neighborhood is $50,000. Comment on your friendʹs suggestion. A) Based on this printout, all you can say is that the mean sale price might be $50,000. B) Your friend is wrong, and you are 98% certain. C) Your friend is correct, and you are 98% certain. D) Your friend is correct, and you are 100% certain. 10) To select the correct Studentʹs t-distribution requires knowing the degrees of freedom. How many degrees of freedom are there for a sample of size n? A) n - 1 B) n C) n + 1 D) x - μ s/ n 11) True or False: Every Studentʹs t-distribution with n < N, n the number in the sample and N the number in the population, will be less peaked and have thinner tails. A) False B) True 12) The area under the graph of every Studentʹs t-distribution is A) 1 B) Less than the standard normal distribution C) Greater than the standard normal distribution D) Area of the standard normal distribution s/ n 13) Which of the following is not a characteristic of Studentsʹ t-distribution? A) mean of 1 B) symmetric distribution C) depends on degrees of freedom. D) For large samples, the t and z distributions are nearly equivalent. 3 Determine t-values. Find the t-value. 14) Let t0 be a specific value of t. Find t0 such that the statement is true: P(t t0) = 0.01 where df = 20. A) B) C) D) ) Find the t-value such that the area in the right tail is with 28 degrees of freedom. A) B) C) D) Page 8

9 16) Find the t-value such that the area left of the t-value is 0.01 with 8 degrees of freedom. A) B) C) D) ) Find the critical t-value that corresponds to 99% confidence and n = 10. A) B) C) D) ) Find the critical t-value that corresponds to 95% confidence and n = 16. A) B) C) D) ) Find the critical t-value that corresponds to 90% confidence and n = 15. A) B) C) D) Construct and interpret a confidence interval for a population mean. 20) How much money does the average professional hockey fan spend on food at a single hockey game? That question was posed to 10 randomly selected hockey fans. The sampled results show that sample mean and standard deviation were $15.00 and $2.65, respectively. Use this information to create a 95% confidence interval for the mean. Express the answer in the form x ± tα/2(s/ n). A) 15 ± 2.262(2.65/ 10) B) 15 ± 2.228(2.65/ 10) C) 15 ± 2.201(2.65/ 10) D) 15 ± 1.833(2.65/ 10) 21) Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal distribution. A sample of 20 part-time workers had mean annual earnings of $3120 with a standard deviation of $677. Round to the nearest dollar. A) ($2803, $3437) B) ($1324, $1567) C) ($2135, $2567) D) ($2657, $2891) 22) Construct a 90% confidence interval for the population mean, μ. Assume the population has a normal distribution. A sample of 15 randomly selected math majors has a grade point average of 2.86 with a standard deviation of Round to the nearest hundredth. A) (2.51, 3.21) B) (2.41, 3.42) C) (2.37, 3.56) D) (2.28, 3.66) 23) Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal distribution. A sample of 25 randomly English majors has a mean test score of 81.5 with a standard deviation of Round to the nearest hundredth. A) (77.29, 85.71) B) (56.12, 78.34) C) (66.35, 69.89) D) (87.12, 98.32) 24) Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal distribution. A random sample of 16 lithium batteries has a mean life of 645 hours with a standard deviation of 31 hours. Round to the nearest tenth. A) (628.5, 661.5) B) (876.2, 981.5) C) (531.2, 612.9) D) (321.7, 365.8) 25) Construct a 99% confidence interval for the population mean, μ. Assume the population has a normal distribution. A group of 19 randomly selected employees has a mean age of 22.4 years with a standard deviation of 3.8 years. Round to the nearest tenth. A) (19.9, 24.9) B) (16.3, 26.9) C) (17.2, 23.6) D) (18.7, 24.1) 26) Construct a 98% confidence interval for the population mean, μ. Assume the population has a normal distribution. A study of 14 car owners showed that their average repair bill was $192 with a standard deviation of $8. Round to the nearest cent. A) ($186.33, $197.67) B) ($222.33, $256.10) C) ($328.33, $386.99) D) ($115.40, $158.80) Page 9

10 27) Construct a 90% confidence interval for the population mean, μ. Assume the population has a normal distribution. In a recent study of 22 eighth graders, the mean number of hours per week that they played video games was 19.6 with a standard deviation of 5.8 hours. Round to the nearest hundredth. A) (17.47, 21.73) B) (18.63, 20.89) C) (5.87, 7.98) D) (19.62, 23.12) 28) A random sample of 10 parking meters in a resort community showed the following incomes for a day. Assume the incomes are normally distributed. Find the 95% confidence interval for the true mean. Round to the nearest cent. $3.60 $4.50 $2.80 $6.30 $2.60 $5.20 $6.75 $4.25 $8.00 $3.00 A) ($3.39, $6.01) B) ($2.11, $5.34) C) ($4.81, $6.31) D) ($1.35, $2.85) 29) The grade point averages for 10 randomly selected junior college students are listed below. Assume the grade point averages are normally distributed. Find a 98% confidence interval for the true mean. Round to the nearest hundredth A) (1.55, 3.53) B) (0.67, 1.81) C) (2.12, 3.14) D) (3.11, 4.35) 30) A local bank needs information concerning the savings account balances of its customers. A random sample of 15 accounts was checked. The mean balance was $ with a standard deviation of $ Find a 98% confidence interval for the true mean. Assume that the account balances are normally distributed. Round to the nearest cent. A) ($513.17, $860.33) B) ($238.23, $326.41) C) ($326.21, $437.90) D) ($487.31, $563.80) 31) To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette gave a mean nicotine content of 28.5 milligrams and standard deviation of 2.2 milligrams for a sample of n = 9 cigarettes. The FDA claims that the mean nicotine content exceeds 31.2 milligrams for this brand of cigarette, and their stated reliability is 95%. Do you agree? A) No, since the value 31.2 does not fall in the 95% confidence interval. B) Yes, since the value 31.2 does fall in the 95% confidence interval. C) Yes, since the value 31.2 does not fall in the 95% confidence interval. D) No, since the value 31.2 does fall in the 95% confidence interval. 32) What effect will an outlier have on a confidence interval that is based on a small sample size? A) The confidence interval will be wider than an interval without the outlier. B) The interval will be smaller than an interval without the outlier. C) The interval will be the same with or without the outlier. D) The interval will reveal exclusionary data. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 33) In a random sample of 26 laptop computers, the mean repair cost was $127 with a standard deviation of $33. Assume the population has a normal distribution. Construct a 95% confidence interval for the population mean, μ. Suppose you did some research on repair costs for laptop computers and found that the standard deviation is σ = 33. Use the normal distribution to construct a 95% confidence interval for the population mean, μ. Compare the results. Round to the nearest cent. 5 Find the sample size needed for estimating a population mean within a given margin of error. 34) Determine the sample size required to estimate the mean score on a standardized test within 4 points of the true mean with 90% confidence. Assume that s = 15 based on earlier studies. A) 39 B) 7 C) 139 D) 1 Page 10

11 35) A doctor at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 99% confident that her estimate is within 2 ounces of the true mean? Assume that s = 7 ounces based on earlier studies. A) 82 B) 81 C) 10 D) 9 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 36) In order to set rates, an insurance company is trying to estimate the number of sick days that full time workers at a local bank take per year. Based on earlier studies, they will assumed that s = 2.8 days. a) How large a sample must be selected if the company wants to be 98% confident that their estimate is within 1 day of the true mean? b) Repeat part (a) using a 99% confidence interval. Which level of confidence requires a larger sample size? Explain. 37) The grade point averages for 10 randomly selected students in an algebra class with 125 students are listed below. What is the effect on the width of the confidence interval if the sample size is increased to 20? A) The width decreases. B) The width increases. C) The width remains the same. D) It is impossible to tell without more information. 38) The principal at Riverside High School would like to estimate the mean length of time each day that it takes all the buses to arrive and unload the students. How large a sample is needed if the principal would like to assert with 90% confidence that the sample mean is off by, at most, 7 minutes. Assume that s = 14 minutes based on previous studies. A) 11 B) 10 C) 12 D) 13 39) True or False: As the level of confidence increases the number of item to be included in a sample will decrease when the error and the standard deviation are held constant. A) False B) True 9.3 Estimating a Population Standard Deviation 1 Find critical values for the chi-square distribution. 1) Find the critical values, χ α/2 and χ 2 α/2, for 95% confidence and n = 12. A) and B) and C) and D) and ) Find the critical values, χ α/2 and χ 2 α/2, for 90% confidence and n = 15. A) and B) and C) and D) and ) Find the critical values, χ α/2 and χ 2 α/2, for 98% confidence and n = 20. A) and B) and C) and D) and Page 11

12 4) Find the critical values, χ α/2 and χ 2 α/2, for 99% confidence and n = 10. A) and B) and C) and D) and ) True or False: The chi-square distribution is a symmetric distribution for all degrees of freedom. A) False B) True 6) True or False: The chi-square distribution is a symmetric distribution is negative when the degrees of freedom become large. A) False B) True 7) True or False: As the number of degrees of freedom increases, the chi-square distribution becomes more nearly symmetric. A) True B) False 2 Construct and interpret confidence intervals for the population variance and standard deviation. 8) Construct a 95% confidence interval for the population standard deviation σ of a random sample of 15 crates which have a mean weight of pounds and a standard deviation of 10.4 pounds. Assume the population is normally distributed. A) (7.6, 16.4) B) (58.0, 269.0) C) (2.4, 5.1) D) (8.0, 15.2) 9) Assume that the heights of bookcases are normally distributed. A random sample of 16 bookcases in one company have a mean height of 67.5 inches and a standard deviation of 1.7 inches. Construct a 99% confidence interval for the population standard deviation, σ. A) (1.1, 3.1) B) (1.2, 3.2) C) (0.9, 2.4) D) (1.2, 2.9) 10) Assume that the heights of female executives are normally distributed. A random sample of 20 female executives have a mean height of 62.5 inches and a standard deviation of 1.1 inches. Construct a 98% confidence interval for the population variance, σ 2. A) (0.6, 3.0) B) (0.8, 1.7) C) (0.6, 2.7) D) (0.7, 3.2) 11) The mean replacement time for a random sample of 12 cd players is 8.6 years with a standard deviation of 4.9 years. Construct the 98% confidence interval for the population variance, σ 2. Assume the data are normally distributed A) (10.7, 86.5) B) (3.3, 9.3) C) (2.2, 17.7) D) (10.1, 74.0) 12) A student randomly selects 10 paperbacks at a store. The mean price is $8.75 with a standard deviation of $1.50. Construct a 95% confidence interval for the population standard deviation, σ. Assume the data are normally distributed. A) ($1.03, $2.74) B) ($0.43, $1.32) C) ($1.43, $2.70) D) ($1.76, $3.10) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 13) The July utility bills (in dollars) of 20 randomly selected homeowners in one city are listed below. Construct a 99% confidence interval for the variance, σ 2. Assume the population is normally distributed Page 12

13 14) The June precipitation (in inches) for 10 randomly selected cities are listed below. Construct a 90% confidence interval for the population standard deviation, σ. Assume the data are normally distributed A) (0.81, 1.83) B) (0.32, 0.85) C) (0.53, 1.01) D) (1.10, 2.01) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 15) A container of soda is supposed to contain 1000 milliliters of soda. A quality control manager wants to be sure that the standard deviation of the soda containers is less than 20 milliliters. He randomly selects 10 cans of soda with a mean of 997 milliliters and a standard deviation of 32 milliliters. Use these sample results to construct a 95% confidence interval for the true value of σ. Does this confidence interval suggest that the variation in the soda containers is at an acceptable level? 16) True or False? When constructing a (1 - α) 100% confidence interval for a population variance σ 2, the population from which the random sample is selected can have any distribution. A) False B) True 17) The best point estimate for the standard deviation of a population is A) The standard deviation of the sample. B) The variance of the population. C) The variance of the sample. D) (n - 1)s2 σ Putting It Together: Which Procedure Do I Use? 1 Determine the appropriate confidence interval to construct. 1) In a random sample of 60 dog owners enrolled in obedience training, it was determined that the mean amount of money spent per owner was $ per class. Assuming the population standard deviation of the amount spent per owner is $12, construct and interpret a 95% confidence interval for the mean amount spent per owner for an obedience class. A) ($106.29, $112.37); we are 95% confident that the mean amount spent per dog owner for a single obedience class is between $ and $ B) ($106.78, $111.88); we are 95% confident that the mean amount spent per dog owner for a single obedience class is between $ and $ C) ($106.23, $112.43); we are 95% confident that the mean amount spent per dog owner for a single obedience class is between $ and $ D) ($106.74, $111.92); we are 95% confident that the mean amount spent per dog owner for a single obedience class is between $ and $ Page 13

14 2) A survey of 1010 college seniors working towards an undergraduate degree was conducted. Each student was asked, ʺAre you planning or not planning to pursue a graduate degree?ʺ Of the 1010 surveyed, 658 stated that they were planning to pursue a graduate degree. Construct and interpret a 98% confidence interval for the proportion of college seniors who are planning to pursue a graduate degree. A) (0.616, 0.686); we are 98% confident that the proportion of college seniors who are planning to pursue a graduate degree is between and B) (0.620, 0.682); we are 98% confident that the proportion of college seniors who are planning to pursue a graduate degree is between and C) (0.621, 0.680); we are 98% confident that the proportion of college seniors who are planning to pursue a graduate degree is between and D) (0.612, 0.690); we are 98% confident that the proportion of college seniors who are planning to pursue a graduate degree is between and Construct a 95% Z-interval or a 95% t-interval about the population mean. Assume the data come from a population that is approximately normal with no outliers. 3) The heights of 20- to 29-year-old females are known to have a population standard deviation σ = 2.7 inches. A simple random sample of n = 15 females 20 to 29 years old results in the following data: A) (64.98, 67.72); we are 95% confident that the mean height of 20 - to 29-year-old females is between and inches. B) (64.85, 67.85); we are 95% confident that the mean height of 20 - to 29-year-old females is between and inches. C) (65.12, 67.58); we are 95% confident that the mean height of 20 - to 29-year-old females is between and inches. D) (65.20, 67.50); we are 95% confident that the mean height of 20 - to 29-year-old females is between and inches. 4) Fifteen randomly selected men were asked to run on a treadmill for 6 minutes. After the 6 minutes, their pulses were measured and the following data were obtained: A) (93.7, 107.1); we are 95% confident that the mean pulse rate of men after 6 minutes of exercise is between 93.7 and beats per minute. B) (94.9, 105.9); we are 95% confident that the mean pulse rate of men after 6 minutes of exercise is between 94.9 and beats per minute. C) (94.2, 106.6); we are 95% confident that the mean pulse rate of men after 6 minutes of exercise is between 94.2 and beats per minute. D) (95.2, 105.6); we are 95% confident that the mean pulse rate of men after 6 minutes of exercise is between 95.2 and beats per minute. Page 14

15 9.5 Estimating with Bootstrapping 1 Explain the general bootstrap algorithm. 1) If we wish to obtain a 98% confidence interval of a parameter using the bootstrap method, which percentiles of the resampled distribution will form the lower and upper bounds of the interval? A) 1, 99 B) 2, 98 C) 2, 99 D) 1, 98 2) A random sample of 20 electricians is obtained and the monthly income is recorded for each one. A researcher plans to use the bootstrap method with 1000 resamples to obtain a 90% confidence interval for the mean monthly income of all electricians. Which of the following is not true of the resamples? A) Each resample will be selected from the population. B) Each resample will be selected with replacement. C) Each resample will be selected from the original sample. D) Each resample will be of the same size as the original sample. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 3) The table shows the monthly rents (in dollars) for 10 studio apartments selected randomly from all studio apartments in one city Explain the algorithm in using the bootstrap method with 1000 resamples to obtain a 90% confidence interval for the mean monthly rent of all studio apartments in the city. 4) A college nurse obtained a random sample of 20 students from the college. Each student was asked if they were taking antidepressants. In the data, a 1 indicates the student is taking antidepressants and a 0 indicates they are not taking antidepressants Treat these data as a simple random sample of all students at the college. Explain the algorithm in using the bootstrap method with 1000 resamples to obtain a 99% confidence interval for the proportion of all students at the college who are taking antidepressants. Page 15

16 Ch. 9 Estimating the Value of a Parameter Answer Key 9.1 Estimating a Population Proportion 1 Obtain a point estimate for the population proportion. 1) A 2) A 3) A 4) A 5) A 6) A 7) A 2 Construct and interpret a confidence interval for the population proportion. 8) A 9) A 10) (0.315, 0.408) 11) (0.197, 0.280) 12) It is not practical to find the confidence interval. It is necessary that np^(1 - p^) 10 to insure that the distribution of p^ be normal. (np^(1 - p^) = 1.6) 13) A 14) A 15) A 16) A 17) A 18) A 3 Find the sample size needed for estimating a population proportion within a given margin of error. 19) A 20) A 21) A 22) A 23) A 24) a) 3394 b) ) A 26) A 27) A 28) A 29) A 30) A 31) A 9.2 Estimating a Population Mean 1 Obtain a point estimate for the population mean. 1) A 2 State properties of Studentʹs t-distribution. 2) A 3) A 4) A 5) A 6) A 7) A 8) A 9) A 10) A Page 16

17 11) A 12) A 13) A 3 Determine t-values. 14) A 15) A 16) A 17) A 18) A 19) A 4 Construct and interpret a confidence interval for a population mean. 20) A 21) A 22) A 23) A 24) A 25) A 26) A 27) A 28) A 29) A 30) A 31) A 32) A 33) ($113.67, $140.33); ($114.32, $139.68), The t-confidence interval is wider. 5 Find the sample size needed for estimating a population mean within a given margin of error. 34) A 35) A 36) a) 43 b) 52; A 99% confidence interval requires a larger sample than a 98% confidence interval because more information is needed from the population to be 99% confident. 37) A 38) A 39) A 9.3 Estimating a Population Standard Deviation 1 Find critical values for the chi-square distribution. 1) A 2) A 3) A 4) A 5) A 6) A 7) A 2 Construct and interpret confidence intervals for the population variance and standard deviation. 8) A 9) A 10) A 11) A 12) A 13) s = $1.73; ($1.47, $8.31) 14) A 15) The 95% confidence interval is (22.01, 58.42). Because this interval does not contain 20, the standard deviation is not at an acceptable level. 16) A Page 17

18 17) A 9.4 Putting It Together: Which Procedure Do I Use? 1 Determine the appropriate confidence interval to construct. 1) A 2) A 3) A 4) A 9.5 Estimating with Bootstrapping 1 Explain the general bootstrap algorithm. 1) A 2) A 3) The sample data is treated as the population. A computer is used to obtain 1000 independent resamples of size n = 10 with replacement from the sample data. For each resample, the sample mean is obtained. The lower bound of the confidence interval is the 5th percentile of the 1000 sample means and the upper bound is the 95th percentile of the 1000 sample means. 4) The sample data is treated as the population. A computer is used to obtain 1000 independent resamples of size n = 20 with replacement from the sample data. For each resample, the sample proportion of students taking antidepressants is obtained. The lower bound of the confidence interval is the 0.5th percentile of the 1000 sample proportions and the upper bound is the 99.5th percentile of the 1000 sample proportions. Page 18