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550.111 Statistical Analysis I  Spring 2007
Midterm #3 version A
Name
1.
Suppose a random sample of size
n
measurements is taken from a normally distributed popu
lation with unknown mean
μ
and unknown standard deviation
σ
. The sample mean and sample
standard deviation are
x
n
= 110 and
s
= 20, respectively. The following are separate question
unless otherwise noted.
(a) [10 pt] If
n
= 225, construct a 95% conﬁdence interval for the population mean
μ
, and then
interpret the meaning of this interval.
(b) [10 pt] If
n
= 7, construct a 95% conﬁdence interval for the population mean
μ
.
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A statistics professor wishes to test if the mean student exam scores on a standardized sta
tistics test diﬀers from that of the national average of 76. Of the 120 students taking this exam
it was found that the sample mean exam score was 79 with a sample standard deviation of 12.
(a) [5 pt] Write down the null and alternative hypotheses for this situation. Please label each
hypothesis appropriately.
(b) [5 pt] Write down the appropriate test statistic to use in this situation.
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 Spring '10
 Jooe

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