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.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '09
 AnthonyChan
 Normal Distribution, Null hypothesis, Suggested Solution Question

Click to edit the document details