Suppose the mean of a population is mu = 22. A researcher (who does not know tha

Question

Suppose the mean of a population is mu = 22. A researcher (who does not know that mu = 22) selects a random sample of size N from this population. Then she constructs a 95% confidence interval of the population mean. The true population mean and the researcher's 95% confidence interval of the population mean are shown in the following graph. Use the graph to answer the questions that follow. Use the grey star to mark the mean of the sample. (Be sure to place the star on the horizontal blue line segment that represents the confidence interval.) The sample mean is x bar = To construct the confidence interval, the quantity t_ S_x bar (called the margin of error) is subtracted from and added to the sample mean. In this case, t_ S_x bar = Suppose that the researcher uses the same sample but decides to construct a 85% confidence interval of the mean of the population. Compared with the center of the 95% confidence interval, the center of the 85% confidence interval ______. Compared to the 95% confidence interval, the 85% confidence interval _______. At the same confidence level, _______ in the sample size would have a similar effect on the width of the confidence interval as changing the confidence level from 95% to 85%.

Explanation / Answer

a) Here 95% Interval is 23 to 30

So, Mean-Margin of error = 23

Mean+Margin of error = 30

Mean = 26.5

Margin of error = 3.5

So, Sample Mean = 26

tcric*Sx = 3.5

b) For 85% Interval

85% Will be same as 95% Interval

Compared to 95% Interval, 85% Confidence Interval will be shorter

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