5
ISMT 111 Fall 05 Final Exam
Suggested solution
Question 1:
(a)
The Hypothesis statement is H
0
:
μ
=23 vs H
1
μ
>23. Naturally we need to assume that that
either the data are normally distributed in which case we assume that the CLT applies.
The sample size n=56 is large enough and we can use the Ztest and the test statistic is
Z=
56 (23.5 – 23)/10.2=.367.
We can use the normal table to find the critical value of 1.645 at alpha =.05. In this case since
.367<1.645 we cannot reject the null hypothesis and must conclude that the evidence
indicates that their claim is false.
(b)
The 95% confidence interval is approximately
23.5
±
2.67
(c)
To find A, solve the equation
56 (23.5 – A)/10.2
≥
1.645, the solution is
A
≤
21.258.
Hence set A=21.
Note: Question (c) can be adjusted for different values of the standard deviation.
Question 2:
(a)
Using the formula
for the differences where the population variances are assumed
equal but unknown and the populations are normally distributed.
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 Spring '09
 AnthonyChan
 Normal Distribution, Null hypothesis, Suggested Solution Question

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