6.2 Margin of error and the confidence interval. A study of stress on the campus of your university using the College Undergraduate Stress Scale (CUSS) reported an average stress level of 1123 (a higher score indicating more stress) with a margin of error of 43 for 95% confidence. The study was based on a random sample of 400 undergraduates. a. Give the 95% confidence interval. b. If you wanted 99% confidence for the same study, would your margin of error be greater than, equal to, or less than 437 Explain your answer. 6.3 Changing the sample size. Consider the setting of the previous exercise. Suppose that the sample mean is again 1123, and the population standard deviation is 441. Make a diagram similar to Figure 6.5 (page 338) that illustrates the effect of sample size on the width of a 95% interval. Use the following sample sizes: 100, 144, 225, 324, and 400. Summarize what the diagram shows. 6.4 Changing the confidence level. Consider the setting of the previous two exercises. Suppose that the sample mean is still 1123, the sample size is 400, and the population standard deviation is 441. Make a diagram similar to Figure 6.6 (page 339) that illustrates the effect of the confidence level on the width of the interval. Use 80%, 90%, 95%, and 99%. Summarize what the diagram shows. n = 500 n = 2000 Introduction to the Practice of W.H. Freeman and Company Statistics, 10e, @ 2021 Moore/Mccabe/Craig. 1300 1400 1500 1600 1700 1800 1900 FIGURE 6.5 Confidence intervals for n = 500 and n = 2000, Examples 6.4 and 6.5. A sample size four times as large results in a confidence interval that is one-half as wide. . 09% s g 3 confidence B g SENSE o GENE 95% $05 confidence 8 388 Sz g5Es % = Ir E:Ea 1400 1500 1600 1700 1800 FIGURE 6.6 Confidence intervals, Examples 6.4 and 6.6. The larger the value of C, the wider the interval