Question

Suppose an experiment is conducted where 100 students at BU are measured and their average height is found to be 67.45 inches, and the (sample) standard deviation to be 2.93 inches. Since 100 is a large sample, we use the sample standard deviation as an estimate of the population standard deviation. We may assume that heights are normally distributed.

(a) Suppose that you want to report the 95.45...% confidence interval (i.e., exactly 2 standard deviations). Give the results of this experiment.

(b) Repeat (a) but for the 99.73... % (exactly 3 standard deviations) confidence interval.

(c) Now suppose you want to report the precisely 95.0% confidence interval (which will be slightly less than 2 standard deviations -- find out the exact figure) Repeat (a) using this confidence interval.

(d) Repeat (c) but for the precisely 99.0% confidence interval.

Answer 1

a) Mean () = 67.45
Sample size (n) = 100
Standard deviation (s) = 2.93
Confidence interval(in %) = 95.45
z @ 95.45% = 2.001
Since we know that

Required confidence interval =
Required confidence interval = (67.45-0.5863, 67.45+0.5863)
Required confidence interval = (66.8637, 68.0363)
b) Confidence interval(in %) = 99.73
z @ 99.73% = 2.995
Required confidence interval =
Required confidence interval = (67.45-0.8775, 67.45+0.8775)
Required confidence interval = (66.5725, 68.3275)

c) Confidence interval(in %) = 95
z @ 95.0% = 1.96
Required confidence interval =
Required confidence interval = (67.45-0.5743, 67.45+0.5743)
Required confidence interval = (66.8757, 68.0243)

d) Confidence interval(in %) = 99
z @ 99.0% = 2.576\
Required confidence interval =
Required confidence interval = (67.45-0.7548, 67.45+0.7548)
Required confidence interval = (66.6952, 68.2048)
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