. Properties of a confidence interval Aa Aa Suppose the mean of a population is
ID: 3375502 • Letter: #
Question
. Properties of a confidence interval Aa Aa Suppose the mean of a population is ?-61. A researcher (who does not know that ? 61) selects a random sample of size n from this population. Then she constructs an 80% confidence interval of the population mean. The true population mean and the researcher's 80% confidence interval of the population mean are shown in the following graph. Use the graph to answer the questions that follow. Sample Mean 80% Confidence Interval of the Population Mean True Population Mean 55 56 57 58 59 60 61 62 63 665 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 tsu is subtracted from and added to the sample mean. In this case, ts Suppose that the researcher uses the same sample but decides to of the population. construct a 90% confidence interval of the mean Compared with the center of the 80% confidence interval, the center of the 90% confidence interval Compared to the 80% confidence interval, the 90% confidence interval At the same confidence level, confidence interval as changing the confidence level from 80% to 90%. in the sample size wouldExplanation / Answer
Sol:
a)
The grey star (sample mean) must be midway between the confidence interval, that is between 56 and 62.
Hence, the grey star has to be placed at = 59 [ANSWER]
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b)
Here,
t*sM = upper bound - sample mean = 62 - 59 = 3 [ANSWER]
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c)
Compared with the center of the 80% confidence interval, the center of the 90% confidence interval [IS THE SAME.]
Compared to the 80% confidence interval, the 90% 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 80% to 90%.
This is so because increasing confidence levels makes the interval wider, and so is decreasing sample size.
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