Solved: Determining Sample Size. In Exercises 1922, assume that each sample is a simple

LDL Cholesterol Using the 40 LDL cholesterol levels of women listed in Data Set 1, we get this 95% confidence interval estimate: 916.591 < 2 < 2252.119 , and the units of measurement are ( mg / dL ) 2 . Identify the corresponding confidence interval estimate of and include the appropriate units. Given that the original values are whole numbers, round the limits using the roundoff rule given in this section. Write a statement that correctly interprets the confidence interval estimate of .

Expressing Confidence Intervals Example 2 showed how the statistics of n = 22 and s = 14.3 result in this 95% confidence interval estimate of : 11.0 < < 20.4 . That confidence interval can also be expressed as (11.0, 20.4), but it cannot be expressed as 15.7 4.7 . Given that 15.7 4.7 results in values of 11.0 and 20.4, why can't we express the confidence interval as 15.7 4.7 ?

Pick 4 Lottery The dotplot below depicts individual digits selected in the Pick 4 lottery from different states. Can the original list of individual sample digits be identified? Can the sample data be used to construct a 95% confidence interval estimate of the population standard deviation for all such digits? Why or why not? d

Normality Requirement What is different about the normality requirement for a confidence interval estimate of and the normality requirement for a confidence interval estimate of ? Finding Critical Values and Confidence Intervals. In Exercises 58, use the given information to find the number of degrees of freedom, the critical values L 2 and R 2 , and the confidence interval estimate of . The samples are from Appendix B and it is reasonable to assume that a simple random sample has been selected from a population with a normal distribution.

Nicotine in Menthol Cigarettes 99% confidence n = 25 , s = 0.24 mg .

Weights of Dollar Coins 99% confidence n = 20 , s = 0.04111 g .

Platelet Counts of Women 95% confidence n = 40 , s = 65.2 .

Earthquake Magnitudes 95% confidence n = 50 , s = 0.587 .

Finding Confidence Intervals. In Exercises 916, assume that each sample is a simple random sample obtained from a population with a normal distribution.. Mean Body Temperature Data Set 3 in Appendix B includes a sample of 106 body temperatures having a mean of 98.20 F and a standard deviation of 0.62 F . Construct a 90% confidence interval estimate of the standard deviation of the body temperatures for the entire population.

Finding Confidence Intervals. In Exercises 916, assume that each sample is a simple random sample obtained from a population with a normal distribution. Chocolate Chip Cookies The Chapter Problem for Chapter 3 includes the numbers of chocolate chips in a sample of 40 Chips Ahoy regular cookies. The mean is 23.95 and the standard deviation is 2.55. Construct a 90% confidence interval estimate of the standard deviation of the numbers of chocolate chips in all such cookies.

Finding Confidence Intervals. In Exercises 916, assume that each sample is a simple random sample obtained from a population with a normal distribution.Antifreeze A container of car antifreeze is supposed to hold 3785 mL of the liquid. Realizing that fluctuations are inevitable, the qualitycontrol manager of the Taconic Chemical Company wants to be quite sure that the standard deviation is less than 30 mL. Otherwise, some containers would overflow while others would not have enough of the coolant. She selects a simple random sample of 24 containers and finds that the mean is 3789 mL and the standard deviation is 42.8 mL. Use these sample results to construct the 99% confidence interval for the true value of . Does this confidence interval suggest that the variation is at an acceptable level?

Finding Confidence Intervals. In Exercises 916, assume that each sample is a simple random sample obtained from a population with a normal distribution.. Pulse Rates of Men and Women Data Set 1 in Appendix B includes 40 pulse rates of men, and those pulse rates have a mean of 67.3 beats per minute and a standard deviation of 10.3 beats per minute. That data set also includes 40 pulse rates of women, and those pulse rates have a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute. a. Construct a 99% confidence interval estimate of the standard deviation of the pulse rates of men. b. Construct a 99% confidence interval estimate of the standard deviation of the pulse rates of women. c. Compare the variation of the pulse rates of men and women. Does there appear to be a difference?

Finding Confidence Intervals. In Exercises 916, assume that each sample is a simple random sample obtained from a population with a normal distribution.. Mercury in Sushi Listed below are the amounts of mercury (in parts per million, or ppm) found in tuna sushi sampled at different stores in New York City. The study was sponsored by the New York Times, and the stores (in order) are D'Agostino, Eli's Manhattan, Fairway, Food Emporium, Gourmet Garage, Grace's Marketplace, and Whole Foods. Construct a 90% confidence interval estimate of the standard deviation of the amounts of mercury in the population. 0.56 0.75 0.10 0.95 1.25 0.54 0.88

Finding Confidence Intervals. In Exercises 916, assume that each sample is a simple random sample obtained from a population with a normal distribution.Highway Speeds Listed below are speeds (mi/h) measured from southbound traffic on I280 near Cupertino, California (based on data from SigAlert). This simple random sample was obtained at 3:30 p.m. on a weekday. Use the sample data to construct a 95% confidence interval estimate of the population standard deviation. Does the confidence interval describe the standard deviation for all times during the week? 62 61 61 57 61 54 59 58 59 69 60 67

Finding Confidence Intervals. In Exercises 916, assume that each sample is a simple random sample obtained from a population with a normal distribution. Promotion and Age Listed below are ages of applicants who were unsuccessful in winning promotion and ages of applicants who were successful in winning promotion (based on data from Debating the Use of Statistical Evidence in Allegations of Age Discrimination by Barry and Boland, American Statistician, Vol. 58, No. 2). Construct 99% confidence interval estimates of the standard deviations of the two populations from which the samples were obtained. Compare the results. What do you conclude? Ages of Unsuccessful Applicants: 34 37 37 38 41 42 43 44 44 45 45 45 46 48 49 53 53 54 54 55 56 57 60 Ages of Successful Applicants: 33 36 37 38 38 39 42 42 43 43 44 44 44 45 45 45 45 46 46 47 47 48 48 49 49 51 51 52 54

Finding Confidence Intervals. In Exercises 916, assume that each sample is a simple random sample obtained from a population with a normal distribution.a. Comparing Waiting Lines The values listed below are waiting times (in minutes) of customers at the Jefferson Valley Bank, where customers enter a single waiting line that feeds three teller windows. Construct a 95% confidence interval for the population standard deviation . 6.5 6.6 6.7 6.8 7.1 7.3 7.4 7.7 7.7 7.7 b. The values listed below are waiting times (in minutes) of customers at the Bank of Providence, where customers may enter any one of three different lines that have formed at three teller windows. Construct a 95% confidence interval for the population standard deviation . 4.2 5.4 5.8 6.2 6.7 7.7 7.7 8.5 9.3 10.0 c. Interpret the results found in parts (a) and (b). Do the confidence intervals suggest a difference in the variation among waiting times? Which arrangement seems better: the singleline system or the multipleline system?

Using Large Data Sets from Appendix B. In Exercises 17 and 18, use the data set from Appendix B. Assume that each sample is a simple random sample obtained from a population with a normal distribution Penny Weights Refer to Data Set 21 in Appendix B and use the weights of the post1983 pennies to construct a 98% confidence interval estimate of the standard deviation of the weights of all post1983 pennies.

Using Large Data Sets from Appendix B. In Exercises 17 and 18, use the data set from Appendix B. Assume that each sample is a simple random sample obtained from a population with a normal distributionAges of Presidents Refer to Data Set 12 in Appendix B and use the ages (years) of the presidents at the times of their inaugurations. Treating the data as a sample, construct a 98% confidence interval estimate of the standard deviation of the population of all such ages.

Determining Sample Size. In Exercises 1922, assume that each sample is a simple random sample obtained from a normally distributed population. Use Table 72 to find the indicated sample size.. IQ of Statistics Professors You want to estimate for the population of IQ scores of statistics professors. Find the minimum sample size needed to be 99% confident that the sample standard deviation s is within 1% of . Is this sample size practical?

Determining Sample Size. In Exercises 1922, assume that each sample is a simple random sample obtained from a normally distributed population. Use Table 72 to find the indicated sample size.McDonald's Waiting Times You want to estimate for the population of waiting times at McDonald's driveup windows, and you want to be 95% confident that the sample standard deviation is within 20% of . Find the minimum sample size. Is this sample size practical?

Determining Sample Size. In Exercises 1922, assume that each sample is a simple random sample obtained from a normally distributed population. Use Table 72 to find the indicated sample size.Flight Delays You want to estimate the standard deviation of arrival delays for American Airlines flights from Chicago to Miami. Find the minimum sample size needed to be 95% confident that the sample standard deviation is within 5% of the population standard deviation. A histogram of a sample of those arrival delays suggests that the distribution is skewed, not normal. How does the distribution affect the sample size?

Determining Sample Size. In Exercises 1922, assume that each sample is a simple random sample obtained from a normally distributed population. Use Table 72 to find the indicated sample size.U.S. Incomes You want to estimate the standard deviation of the population of current annual incomes of adults in the United States. Find the minimum sample size needed to be 99% confident that the sample standard deviation is within 5% of the population standard deviation. Does the population of incomes have a normal distribution, and how is the sample size affected by the distribution?

Finding Critical Values In constructing confidence intervals for or 2 , Table A4 can be used to find the critical values L 2 and R 2 only for select values of n up to 101, so the number of degrees of freedom is 100 or smaller. For larger numbers of degrees of freedom, we can approximate L 2 and R 2 by using 2 = 1 2 [ z / 2 + 2 k 1 ] 2 where k is the number of degrees of freedom and z / 2 is the critical z score described in Section 72. Use this approximation to find the critical values L 2 and R 2 for Exercise 9. How do the results compare to the actual critical values of 82.354 and 129.918?