Chapter 8 From Samples to Population Active Learning Questions For use with classroom response systems Copyright В© 2009 Pearson Education, Inc. Slide 8 - 1 Nine employees of a company are selected at random and asked how far they commute to work each day. The distances (in miles) are as follows: 32, 18, 44, 29, 25, 38, 5, 48, 12. Estimate the mean commute distance of all employees of the company. a. It is not possible to estimate the population mean from this sample data. b. 26.7 miles c. 27.9 miles d. 29 miles Slide 8 - 2 The ages of employees at a particular company have a mean of 39. The distribution of sample means for samples of size 200 is normal with a mean of 39 and a standard deviation of 0.79. Suppose you take a sample of size 200 employees from the company and find that their mean age is 41.3. How many standard deviations is the sample mean above the mean of the sampling distribution? a. 2.3 b. 2.9 c. 41.2 d. 3.2 Slide 8 - 3 Among a random sample of 150 employees of a particular company, the mean commute distance is 28.1 miles. This mean lies 0.7 standard deviations below the mean of the sampling distribution. If a second sample of 150 employees is selected, what is the probability that for the second sample, the mean commute distance will be at least 28.1 miles? a. 0.7580 b. 0.5000 c. 0.2420 d. 0.2743 Slide 8 - 4 In one city, there are a total of 1640 5-year-old children of whom 553 live with one parent only. Among a sample of 600 of the 5-year-old children from this city, 223 live with one parent only. Find the sample proportion of 5-year-old children who live with only one parent. a. 0.37 b. 0.34 c. 0.4 d. 223 Slide 8 - 5 There are 13,339 eligible voters in one town. Among a sample of 828 eligible voters from this town, 396 say that they plan to vote in the next mayoral election. Based on this sample, estimate the number of eligible voters in this town who will not vote in the next mayoral election. a. 6959 b. 432 c. 6380 d. 0.52 Slide 8 - 6 12% of the residents of one town are aged over 70. The distribution of sample proportions for samples of 140 residents is normal with a mean of 0.12 and a standard deviation of 0.027. Suppose that you select a sample of 140 residents and find that the proportion aged over 70 in the sample is 0.08. What is the probability that a second sample would be selected with a proportion greater than 0.08? a. 0.08 b. 0.12 c. 0.0668 d. 0.9332 Slide 8 - 7 What is the margin of error for a sample size = 1225, sample mean = 214, and standard deviation = 98? a. 0.56 b. 5.6 c. 56 d. 560 Slide 8 - 8 At one hospital, a random sample of 100 women giving birth to their first child is selected. Among this sample, the mean age was 25.7 with a standard deviation of 5.1. Estimate the mean age of all women giving birth to their first child at this hospital. Give the 95% confidence interval two decimal places. a. 24.68 to 26.72 b. 20.6 to 30.8 c. 25.21 to 26.21 d. 15.5 to 35.9 Slide 8 - 9 A medical researcher wishes to estimate the mean systolic blood pressure of heart surgery patients the day following surgery. She desires a margin of error of 1.6 mm Hg. Past studies suggest that a population standard deviation of 43 mm Hg is reasonable. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy. a. 53.75 b. 0.0744 c. 2889 d. 137.6 Slide 8 - 10 A government survey conducted to estimate the mean price of houses in a metropolitan area is designed to have a margin of error of $8000. Pilot studies suggest that the population standard deviation is $56,000. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy. a. 196 b. 225 c. 256 d. 289 Slide 8 - 11 A researcher collects the weight (in pounds) of a random sample of 32 new born babies, born at a particular hospital. Give the 95% confidence interval to two decimal places. The sample mean is 7.19 pounds and the standard deviation is 0.844 pounds. a. 7.16 to 7.22 b. 7.04 to 7.33 c. 7.14 to 7.24 d. 6.89 to 7.49 Slide 8 - 12 A researcher wishes to estimate the proportion of left-handers among a certain population. In a random sample of 900 people from the population, 74% are left-handed. Find the margin of error for the 95% confidence interval. a. 0.0146 b. 0.0292 c. 0.0493 d. 0.0173 Slide 8 - 13 A researcher wishes to estimate the proportion of left-handers among a certain population. In a random sample of 990 people from the population, 36.4% are left-handed. Find the 95% confidence interval for the population proportion of left-handers to four decimal places. a. 0.3334 to 0.3946 b. 0.3487 to 0.3793 c. 0.6054 to 0.6666 d. 0.6207 to 0.6513 Slide 8 - 14 A population proportion is to be estimated. Estimate the minimum sample size needed to achieve a margin of error of E = 0.056 with a 95% degree of confidence. a. 31.9 b. 319 c. 18 d. 180 Slide 8 - 15 The college daily reported: вЂњ600 students living in university housing were polled. 360 said that they were satisfied with their living conditions. Based on this survey we conclude that 60% of students living in dormitories are satisfied. The margin of error of the study is 4 percentage points (with a 95% degree of confidence).вЂќ Which statement is correct? a. There is not enough information to determine whether the margin of error is consistent with the sample size. b. The stated margin of error could have been achieved with a smaller sample size. c. A larger sample size should be used to achieve the stated margin of error. d. The margin of error is consistent with sample size. Slide 8 - 16

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