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9. Telephone Interviews: Survey The National Study of the Changing Work Force conducted an extensive survey of 2958 wage and salaried workers on issues ranging from relationships with their bosses to household chores. The data were gathered through hour-long telephone interviews with a nationally representative sample (The Wall Street Journal). In response to the question “What does success mean to you?” 1538 responded, “Personal satisfaction from doing a good job.” Let p be the population proportion of all wage and salaried workers who would respond the same way to the stated question. Find a 90% confidence interval for p.

10. Telephone Interviews: Survey How large a sample is needed in Problem 9 if we wish to be 95% confident that the sample percentage of those equating success with personal satisfaction is within 1% of the population percentage? Hint: Use p < 0.52 as a preliminary estimate.

Peppers The following data represent soil water content (percent water by volume) for independent random samples of soil taken from two experimental fields growing bell peppers

Agricultural, Biological, and Environmental Statistics). Note: These data are also available for download at the Componion Sites for this Text. Soil water content from field I: x1; n1 5 72 15.1 11.2 10.3 10.8 16.6 8.3 9.1 12.3 9.1 14.3 10.7 16.1 10.2 15.2 8.9 9.5 9.6 11.3 14.0 11.3 15.6 11.2 13.8 9.0 8.4 8.2 12.0 13.9 11.6 16.0 9.6 11.4 8.4 8.0 14.1 10.9 13.2 13.8 14.6 10.2 11.5 13.1 14.7 12.5 10.2 11.8 11.0 12.7 10.3 10.8 11.0 12.6 10.8 9.6 11.5 10.6 11.7 10.1 9.7 9.7 11.2 9.8 10.3 11.9 9.7 11.3 10.4 12.0 11.0 10.7 8.8 11.1 Soil water content from field II: x2; n2 5 80 12.1 10.2 13.6 8.1 13.5 7.8 11.8 7.7 8.1 9.2 14.1 8.9 13.9 7.5 12.6 7.3 14.9 12.2 7.6 8.9 13.9 8.4 13.4 7.1 12.4 7.6 9.9 26.0 7.3 7.4 14.3 8.4 13.2 7.3 11.3 7.5 9.7 12.3 6.9 7.6 13.8 7.5 13.3 8.0 11.3 6.8 7.4 11.7 11.8 7.7 12.6 7.7 13.2 13.9 10.4 12.8 7.6 10.7 10.7 10.9 12.5 11.3 10.7 13.2 8.9 12.9 7.7 9.7 9.7 11.4 11.9 13.4 9.2 13.4 8.8 11.9 7.1 8.5 14.0 14.2 (a) Use a calculator with mean and standard deviation keys to verify that x1 < 11.42, s1 < 2.08, x2 < 10.65, and s2 < 3.03.

(b) Let m1 be the population mean for x1 and let m2 be the population mean for x2. Find a 95% confidence interval for m1 2 m2.

(c) Interpretation Explain what the confidence interval means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 95% level of confidence, is the population mean soil water content of the first field higher than that of the second field?

(d) Which distribution (standard normal or Student’s t) did you use? Why? Do you need information about the soil water content distributions?

Answer 1