364 Chapter 8 Confidence Intervals 48. Stock prices: The Standard and Poor’s (S&P) 500 is a group of 500 large companies traded on the New York Stock Exchange. Following are prices, in dollars, for a random sample of ten stocks on June 19, 2013. 84.86 8.11 74.23 35.25 13.19 53.55 84.25 201.94 24.68 53.47 Assume the population standard deviation is �� = 50. a. Explain why it is necessary to check whether the population is approximately normal before constructing a confidence interval. n ≤ 30 b. Following is a dotplot of these data. Is it reasonable to assume that the population is approximately normal? No 0 50 100 150 200 250 c. If appropriate, construct a 95% confidence interval for the mean price for all S&P 500 stocks on this day. If not appropriate, explain why not. Not appropriate 49. High energy: A random sample of energy drinks had the following amounts of caffeine per fluid ounce. 14.2 8.3 80.8 6.7 3.6 13.7 12.9 11.5 24.7 9.5 Assume the population standard deviation is �� = 24. a. Explain why it is necessary to check whether the population is approximately normal before constructing a confidence interval. n ≤ 30 b. Following is a dotplot of these data. Is it reasonable to assume that the population is approximately normal? No 0 10 20 30 40 50 60 70 80 90 c. If appropriate, construct a 95% confidence interval for the mean amount of caffeine in all energy drinks. If not appropriate, explain why not. Not appropriate 50. Let’s shake on it: A random sample of 12-ounce milkshakes from 14 fast-food restaurants had the following number of calories. 504 399 580 476 450 591 510 700 608 472 642 613 473 375 Assume the population standard deviation is �� = 90. a. Explain why it is necessary to check whether the population is approximately normal before constructing a confidence interval. n ≤ 30 b. Following is a dotplot of these data. Is it reasonable to assume that the population is approximately normal? yes 350 400 450 500 550 600 650 700 750 c. If appropriate, construct a 95% confidence interval for the mean number of calories for all 12-ounce milkshakes sold at fast-food restaurants. If not appropriate, explain why not. (480.93, 575.22) 51. Lifetime of electronics: In a simple random sample of 100 electronic components produced by a certain method, the mean lifetime was 125 hours. Assume that component lifetimes are normally distributed with population standard deviation �� = 20 hours. a. Construct a 98% confidence interval for the mean battery life. (120, 130) b. Find the sample size needed so that a 99% confidence interval will have a margin of error of 3. 295 52. Efficient manufacturing: Efficiency experts study the processes used to manufacture items in order to make them as efficient as possible. One of the steps used to manufacture a metal clamp involves the drilling of three holes. In a sample of 75 clamps, the mean time to complete this step was 50.1 seconds. Assume that the population standard deviation is �� = 10 seconds. a. Construct a 95% confidence interval for the mean time needed to complete this step. (47.8, 52.4) b. Find the sample size needed so that a 98% confidence interval will have margin of error of 1.5. 241 53. Different levels: Joe and Sally are going to construct confidence intervals from the same simple random sample. Joe’s confidence interval will have level 90% and Sally’s will have level 95%. a. Which confidence interval will have the larger margin of error? Or will they both be the same? Sally’s b. Which confidence interval is more likely to cover the population mean? Or are they both equally likely to do so? Sally’s 54. Different levels: Bertha and Todd are going to construct confidence intervals from the same simple random sample. Bertha’s confidence interval will have level 98% and Todd’s will have level 95%. a. Which confidence interval will have the larger margin of error? Or will they both be the same? Bertha’s b. Which confidence interval is more likely to cover the population mean? Or are they both equally likely to do so? Bertha’s 55. Different standard deviations: Maria and Bob are going to construct confidence intervals from different simple random samples. Both confidence intervals will have level 95%. Maria’s sample comes from a population with standard deviation �� = 1, and Bob’s comes from a population with �� = 2. Both sample sizes are the same. a. Which confidence interval will have the larger margin of error? Or will they both be the same? Bob’s b. Which confidence interval is more likely to cover the population mean? Or are they both equally likely to do so? Both equally likely 56. Different standard deviations: Martin and Bianca are going to construct confidence intervals from different simple random samples. Both confidence intervals will have level 99%. Martin’s sample comes from a population with standard deviation �� = 25, and Bianca’s comes from a population with �� = 18. Both sample sizes are the same. a. Which confidence interval will have the larger margin of error? Or will they both be the same? Martin’s b. Which confidence interval is more likely to cover the population mean? Or are they both equally likely to do so? Both equally likely 57. Which interval is which? Sam constructed three confidence intervals, all from the same random sample. The confidence levels are 90%, 95%, and 99%. The confidence intervals are 5.6 < �� < 14.4, 7.2 < �� < 12.8, and 6.6 < �� < 13.4. Unfortunately, Sam has forgotten which confidence interval has which level. Match each confidence interval with its level. 90%: (7.2, 12.8), 95%: (6.6, 13.4), 99%: (5.6, 14.4)
navidi_monk_elementary_statistics_2e_ch7-9
To see the actual publication please follow the link above