2. Confidence Interval Given. Assume I created a 95% confidence interval for the
ID: 3134858 • Letter: 2
Question
2. Confidence Interval Given. Assume I created a 95% confidence interval for the mean hours studied for a test based on a random sample of 100 students. The lower bound of this interval was 6 and the upper bound was 10. Assume that when I created this interval I knew the population standard deviation. Using this information,
(a) Calculate the width of the interval? [Round to 2 decimal places.]
(b) Calculate the margin of error for the interval? [Round to 2 decimal places.]
(c) Calculate the center of the interval? [Round to 2 decimal places.]
(d) What is the sample mean?
(e) Calculate the population standard deviation.
Explanation / Answer
(a) Calculate the width of the interval? [Round to 2 decimal places.]
Width = upper - lower = 10 - 6 = 4 [ANSWER]
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(b) Calculate the margin of error for the interval? [Round to 2 decimal places.]
Margin of error = width/2 = 4/2 = 2 [ANSWER]
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(c) Calculate the center of the interval? [Round to 2 decimal places.]
Center = (upper+lower)/2 = (10+6)/2 = 8 [ANSWER]
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(d) What is the sample mean?
The center is also the sample mean,
sample mean = 8 [ANSWER]
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(e) Calculate the population standard deviation.
Note that
E = z*sigma/sqrt(n)
where E = the margin of error. Hence, as z = 1.96 for a 95% confidence interval,
sigma = E*sqrt(n)/z = 2*sqrt(100)/1.96 = 10.20408163 [ANSWER]
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