Answer the questions in the spaces provided on the question sheets. You may refer to any tables and software at any time. Your grade will be based on a combination of completeness and randomly selected problems to grade. The packet is due at the beginning of class on Monday, Oct 8th. You are allowed to work with your fellow students, but DO NOT JUST COPY WORK FROM EACH OTHER.
1. State whether you would perform a matched pairs t-test, a pooled variance t-test, a
t-test for unequal variances, a Z test for two population proportions, or an F-test for two
population variances and briefly explain your answer in each of the following scenarios:
(a) You are interested in determining if there is a statistical difference between the
percentage of voters in California who support rent control vs. the nationwide percentage
of voters who support rent control, and take independent random samples
from each population to compare them.
(b) You are the chief statistician for a pharmaceutical company, and are testing a new
diabetes drug that controls insulin levels in the bloodstream. You anticipate that
factors like weight, age, and sex may drastically affect the drug’s response, so you
pair a placebo group and a treatment group together by matching subjects based
on these traits.
(c) You are the General Manger of the Lakers, and are attempting to choose who to
select with your draft pick this season. The two players you are interested in have
a similar average in points per game, but you are interested in determining if one
player is more consistent than the other.
(d) You are curious about the average age of business majors vs sociology majors at
Cal State LA, and sent out a survey to each department and record the responses
before performing the test.
2. You are the manager of Howlin’ Ray’s Famous Chicken, and have recently opened up a
second location. The original location is in Chinatown, and has a continuous and regular
stream of customers every day. The new location is at the City Walk at Universal
Studios, and has irregular traffic from Monday-Thursday and incredibly high volume
(a) You took a random sample of 34 days at the original location, and found ¯y = 2546
dollars and sy = 567.23 dollars in daily sales. You also took a random sample of 18
days at the new location, and found ¯x = 2347.42 dollars and sx = 3921.4 dollars in
daily sales. Test the null hypothesis σ
x − σ
y = 0 vs. the two-sided alternative at
the α = .05 significance level.
(b) Compute the p-value of the test-statistic from part a)
(c) Based on the introduction and your answers to the previous two parts, in order to
test the null hypothesis µx − µy = 0, is it more appropriate to do a pooled variance
t-test for populations with equal variances, or a t-test for populations with unequal
variances? Briefly explain your choice.
(d) Test the null hypothesis µx − µy = 0 vs the two-sided alternative at the α = .01
significance level using your answer from c)
(e) Construct a 99% confidence interval for the test-statistic you calculated in part d)
(f) An executive is interested in sharing your findings at a meeting. Summarize your
results in comparing the restaurants based on both their variances and their means
in daily sales.
3. You read in a business journal that financial analysts are more liberal than accountants.
In order to investigate this further, you took a simple random sample of 98 finance
majors and found 23 of them identified as Democrats, while a simple random sample of
57 accounting majors contained 13 students who identified as Democrats.
(a) Is there good evidence that this is the case? Support your claim with a one-sided
hypothesis test at the α = .05 significance level.
(b) Form a 90% confidence interval for the test-statistic you calculated in part a)
(c) What is the p-value of the test-statistic in part a)?
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