Suppose the mean of a population is Mu = 51. A researcher (who does not know tha

Question

Suppose the mean of a population is Mu = 51. A researcher (who does not know that Mu = 51) selects a random sample of size n from this population. Then she constructs an 85% confidence interval of the population mean. The true population mean and the researcher's 85% 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.) To construct the confidence interval, the quantity ts_M (called the margin of error) is subtracted from and added to the sample mean. In this case, ts_M = . Suppose that the researcher uses the same sample but decides to construct a 95% confidence interval of the mean of the population. Compared with the center of the 85% confidence interval, the center of the 95% confidence interval ________ . Compared to the 85% confidence interval, the 95% 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 85% to 95%.

Explanation / Answer

a)

The grey star (sample mean) must be midway between the confidence interval, that is between 44 and 52.

Hence, the grey star has to be placed at = 48 [ANSWER]

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b)

Here,

t*sM = upper bound - sample mean = 52 - 48 = 4 [ANSWER]

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c)

Compared with the center of the 85% confidence interval, the center of the 95% confidence interval [IS THE SAME.]

Compared to the 85% confidence interval, the 95% confidence interval is [WIDER.]

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d)

At the same confidence level, [DECREASING] in the sample size would have a similar effect on the width of the confidence interval as changing the confidence level from 85% to 95%.

This is so because increasing confidence levels makes the interval wider, and so is decreasing sample size.

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