Stat 250 Fall 2015 … Exam 2 Solutions
1.
PROPOSAL 127:
Minority or Not?
– A poll is to be taken to estimate the level of support for Proposal 127 by all
homeowners in the city of Ypsilanti.
A large random sample of Ypsilanti homeowners was selected and 36% of
the respondents stated they support Proposal 127.
a.
The intern working on this survey was asked to provide a confidence interval estimate for the proportion for
all homeowners in Ypsilanti that support Proposal 127. The intern correctly computed the 95% confidence
interval estimate of (0.30, 0.42).
However, the interval estimate using a 99% confidence level is also to be
included in the summary report.
Which of the following intervals could be the 99% confidence interval based
on the same survey responses?
Circle one.
[2]
(0.28, 0.44)
(0.27, 0.43)
(0.33, 0.39)
Centered at 0.36 and wider
wider but not centered at 0.36
narrower
b.
The Chamber of Commerce would like to assess if a minority of all Ypsilanti homeowners support Proposal 127.
Based on the survey results, with 95% confidence, it appears the proportion of all Ypsilanti homeowners

supporting Proposal 127 is:

c.
The intern has prepared a number of statements for possible inclusion in the final summary report.
For each
of the following statements, determine if it is correct and could be included in the report or if it is incorrect.
[4]
There is a 95% probability that the confidence interval produced
from this sample contains the proportion of all homeowners in Ypsilanti
that support Proposal 127.
Correct
Not correct
95% of all homeowners in Ypsilanti support Proposal 127.
Correct
Not correct
If we were to repeat this poll many times, we would expect the proportion
for all homeowners in Ypsilanti that support Proposal 127 to fall in 95%
of the 95% confidence intervals.
Correct
Not correct
Based on this poll, the proportion for all homeowners in Ypsilanti that support
Proposal 127 is
estimated
to be 36%, with a 95% margin of error of 6%.
Correct
Not correct
2.
A Study about Changing Major –
Two advisors, Ana and Carlos, are interested in testing whether the proportion
of all students at their college who have changed their major is 0.60, as claimed by the advising office (versus the
rate is not 0.60).
a.
Ana plans to conduct the test using a 10% level of significance, but Carlos wants the significance level lowered
to 5%. For which level of significance will the probability of correctly concluding that the changing major rate

[2]
Circle one:
5%