6.34 Margin of error and the confidence interval. A study based on a sample of s
ID: 3364901 • Letter: 6
Question
6.34 Margin of error and the confidence interval. A study based on a sample of size 30 reported a mean of 82 with a margin of error of 7 for 95% confidence. (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 7? Explain your answer. 6.35 Change the sample size. Consider the setting of the previous exercise. Suppose that the sample mean is again 82 and the population standard eviation is 7. Make a diagram similar to Figure 6.10 (page 309) that illustrates the effect of sample size on the width of a 95% interval. Use the following sample sizes: 10, 20, 40, and 80. Summarize what the diagram shows. 6.36 Change the confidence. Consider the setting of the previous two exercises. Suppose that the sample mean is still 82, the sample size is 30, and the population standard deviation is 7. Make a diagram similar to Figure 6.11 (page 310) 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.Explanation / Answer
6.34
a)
b)
we find std.dev. from the above ME, std. dev. = 19.56
The CI would be
ME = 9.2, this is because of higher value of z
CI for 95% n 30 mean 82 z-value of 95% CI 1.9600 ME = z*SE 7.00000 Lower Limit = Mean - ME 75.00000 Upper Limit = Mean + ME 89.00000 95% CI (75 , 89 )Related Questions
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