Problem Solving
11/08/2007
http://www.rossmanchance.com/applets/Confsim/Confsim.html
1. T/F The sample mean of an SRS equals its corresponding population mean.
2. T/F The length of a 95% CI is longer than a 90%CI based on the same SRS for the same
parameter.
3. T/F A 95% CI, obtained from a valid SRS, for the corresponding population mean can capture
the sample mean approximately 95% of the time.
4. T/F In terms of a given valid SRS, there exists only one valid 95% CI for the corresponding
population mean.
9.55 The article “Selected Characteristics of High-Risk Students and Their Enrollment
Persistence” (Journal of College Student Development [1994]: 54-60) examined factors that affect
whether students stay in college. The following summary statistics are based on data from a
sample of 44 students who did not return to college after the first quarter (the non-persisters) and a
sample of 257 students who did return (the persisters):
Number of Hours Worked per week during the First Quarter
Mean
Standard Deviation
Non-persisters
25.62
14.41
Persisters
18.10
15.31
a.
Suppose the sample of 44 non-persisters is a SRS from the population of all
non-persisters. With z critical value, construct a 98% CI and a 90%CI for the mean
numbers of hours worked per week for non-persisters.
b. Based on the 98%CI in (a), do you think that the mean numbers of hours worked per
week for non-persisters is greater than 21?
c.
Find the 1% percentile for the mean numbers of hours worked per week for
non-persisters.
d. Based on the 90%CI in (a), do you think that the mean numbers of hours worked per
week for non-persisters is greater than 21?
e.
Does the answer for (b) agree with the one for (d)? Why?
f.
Suppose the sample of 257 persisters is a SRS from the population of all persisters. With
z critical value, construct a 98% CI for the mean numbers of hours worked per week for
persisters.
g. Why the 98%CI for persisters is narrower than the one for non-persisters?
h. Suppose the two samples are both SRS with respect to the corresponding populations.
With z critical value, construct a 98% CI for the difference of the mean numbers of hours
worked per week for the two populations.
i.
Based on the 98% CI obtained in (h), can you claim that you are 100% sure that the
difference of the mean numbers of hours worked per week for the two populations is
significant or not zero.
j.
Redo (a) by using t critical value (with degree of freedom = 43), and compare your new
98%CI with the one you obtained in (a). Which one is better? Why?