Are Nuclear Plants Safe? In a Gallup poll of 1038 adults, 47% said that nuclear plants are safe, 49% said that they are not safe, and 4% had no opinion. Construct a 95% confidence interval estimate of the proportion of all adults who say that nuclear plants are safe. Based on the result, can we conclude that fewer than half of all adults say that nuclear plants are safe?

Critical Thinking. In Exercises 17–28, use the data and confidence level to construct a confidence interval estimate of p, then address the given question.

Job Interviews In a Harris poll of 514 human resource professionals, 90% said that the appearance of a job applicant is most important for a good first impression.

a. Among the 514 human resource professionals who were surveyed, how many of them said that the appearance of a job applicant is most important for a good first impression?

Critical Thinking. In Exercises 17–28, use the data and confidence level to construct a confidence interval estimate of p, then address the given question.

Gender Selection Before its clinical trials were discontinued, the Genetics & IVF Institute conducted a clinical trial of the XSORT method designed to increase the probability of conceiving a girl and, among the 945 babies born to parents using the XSORT method, there were 879 girls. The YSORT method was designed to increase the probability of conceiving a boy and, among the 291 babies born to parents using the YSORT method, there were 239 boys. Construct the two 95% confidence interval estimates of the percentages of success. Compare the results. What do you conclude?

In Exercises 7–10, use the same population of {4, 5, 9} that was used in Examples 2 and 5. As in Examples 2 and 5, assume that samples of size n = 2 are randomly selected with replacement.

Sampling Distribution of the Sample Proportion

c. Find the mean of the sampling distribution of the sample proportion of odd numbers.

In Exercises 7–10, use the same population of {4, 5, 9} that was used in Examples 2 and 5. As in Examples 2 and 5, assume that samples of size n = 2 are randomly selected with replacement.

Sampling Distribution of the Sample Proportion

a. For the population, find the proportion of odd numbers.

Control Charts for p. In Exercises 5–12, use the given process data to construct a control chart for p. In each case, use the three out-of-control criteria listed near the beginning of this section and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply.

Li-ion Batteries Rechargeable lithium ion batteries are used for mobile computing devices and portable power systems. Consider batteries manufactured to provide a capacity of 2200 mAh (milliampere hour) with a minimum of 2150 mAh. Batteries not meeting those specifications are defects. Listed below are numbers of defects in batches of 300 randomly selected batteries in each of 12 consecutive days of production. What action should be taken?

4 3 5 8 12 7 11 9 9 7 6 19

Control Charts for p. In Exercises 5–12, use the given process data to construct a control chart for p. In each case, use the three out-of-control criteria listed near the beginning of this section and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply.

Car Batteries Defective car batteries are a nuisance because they can strand and inconvenience drivers, and drivers could be put in danger. A car battery is considered to be defective if it fails before its warranty expires. Defects are identified when the batteries are returned under the warranty program. The Powerco Battery corporation manufactures car batteries in batches of 250, and the numbers of defects are listed below for each of 12 consecutive batches. Does the manufacturing process require correction?

3 4 2 5 3 6 8 9 12 14 17 20

Confidence Interval Assume that we want to use the sample data in Exercise 1 for constructing a confidence interval to be used for testing the given claim.

c. If the resulting confidence interval is -5.8 admissions <ud < -0.9 admissions, what do you conclude?

Overlap of Confidence Intervals In the article “On Judging the Significance of Differences by Examining the Overlap Between Confidence Intervals,” by Schenker and Gentleman (American Statistician, Vol. 55, No. 3), the authors consider sample data in this statement: “Independent simple random samples, each of size 200, have been drawn, and 112 people in the first sample have the attribute, whereas 88 people in the second sample have the attribute.”

a. Use the methods of this section to construct a 95% confidence interval estimate of the difference p1-p2. What does the result suggest about the equality of p1 and p2

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