8. Suppose that 100 randomly selected members of the Karaoke Channel were asked

Question

8. Suppose that 100 randomly selected members of the Karaoke Channel were asked how much time they typically spend on the site during one week. The sample mean was found to be 3.8 hours. Assume that the population standard deviation is knowrn to be -2.9 hour. a, 95% margin of error of the average time. b, 95% confidence interval for the average time on the site. C. Interpret the 95% confidence interval by the way that non statistician can understand. (use one sentence) d. If we reduce the 95% margin of error to 15 minutes, what is the sample size?

Explanation / Answer

8)a) At 95% confidence interval the critical value Z0.975 = 1.96

Margin of error = Z0.975 * (SD/sqrt (n))

= 1.96 * (2.9/sqrt(100))

= 0.5684

B) cinfidence interval = mean +/- margin of error

= 3.8 +/- 0.5684

= 3.2316, 4.3684

C) At 95% cinfidence interval has the 0.95 probability of containing the population mean. 95% of the population distribution is contained in the cinfidence interval.

D) 15min = 0.25 hour

Margin of error = 0.25

Or, Z0.975 * SD/Sqrt (n ) = 0.25

Or, 1.96 * 2.9/sqrt (n) = 0.25

Or, (1.96 * 2.9)/0.25 = Sqrt (n)

Or, sqrt (n) = 22.736

Or, n = 516.93 = 517

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