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MSCI 3710
Final Exam Solutions
Spring 2003
No.
Solution
Version A
1
The historical mean is 29 and we want to see if it is now lower, so it will
be the lefttailed test Ho: µ >= 29
vs.
Ha: µ < 29
B
2
The distribution of the test statistic is t because the population standard
deviation is not given (s=25 is the
sample
standard deviation) and the
sample size is 10 (i.e., less than 30)
B
3
This is a onetail test (left tail).
Look at the t table with alpha=5% and 9
degrees of freedom.
The critical t value is 1.833, for our case it will be
–1.833 to get it on the left tail. So, the rejection area is t* < –1.833
D
4
Since t*(= –1.56) > t critical (= –1.833), we fail to reject the null
hypothesis. So the new mean is not less than 29.
D
5
Here the test is lefttailed and –0.327 < 1.77, so t* < t crit, therefore we
fail to reject the null hypothesis. Alternatively, the pvalue (= 0.374, we
have onetail test) is not smaller than alpha, so fail to reject the null
hypothesis.
So, IDT rates are not lower.
C
6
There are 14 pairs of observations. So, d.f. = 14 – 1 = 13
C
7
Because this is a onetail test, the critical value is t = 1.77
A
8
The correct set of hypotheses for this test is
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 Spring '08
 Dr.Jay

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