Econ Statistics

1. You are conducting a study on the upcoming Democratic presidential primary, and want to know
what proportion of the voting population will cast a vote for Hilary Clinton. You took a simple
random sample of 105 voters, and 62 of the voters indicated they would vote for Hilary Clinton. Let
P denotes the population proportion of Hilary Clinton voters.
(a) What is pˆ?

(b) Test the null hypothesis that P = .5 versus the alternative P > .5 at the α = .05 significance
level

(c) What is the p-value of the test statistic you calculated in b)? Would you reject the null at
α = .04? Would you reject the null at α = .03?

(d) Test the null hypothesis that P = .5 versus the two-sided alternative at the α = .05 significance
level. (Hint: do you need to calculate a new test statistic?)

(e) What is the two-sided p-value of the test statistic?

2. State whether you would use a two-sample Z test for population means, a matched pairs t test, a
two-sample t test for population means with equal variances, or a two-sample t test for population
means with unequal variances in each of the following scenarios. Give a brief explanation as to why
you made your selection:
(a) You are the chief statistican for a pharmaceutical company that’s developing a new diabetes
drug. You want to measure the mean response to the drug and the mean response to a placebo
in order to measure the drug’s effectiveness. In your study, you have split the population into
two groups, one obtaining the treatment and one obtaining the placebo, and then formed pairs
of one participant from each group using a combination of random assignment and matching
based on similar traits.

(b) You are the chief statistician for a pharmaceutical company that’s developing a new drug to
prevent flea bites in dogs. In particular, your company is interested in how the drug will affect
golden retrievers, and specifically if males respond to the drug differently than females. You
obtained random samples from a population of male golden retrievers, and a population of
female golden retrievers, and computed the sample mean and sample standard deviation from
each population.

(c) You are a financial analyst, and your company is trying to choose between two investments.
The variance of the return of each investment is known, but your company wants to know if
either investment has a higher average return. You take a simple random sample of 100 days,
and measured the return of the investment on each of those days, which you used to calculate
a sample mean for each population.

(d) You work in the music industry, and are conducting a study for your record label on how recent
news has affected different demographics. In your study, you take a simple random sample from
a population of men 50 and over, and a simple random sample from a population of girls age
10-15, and measure their response to the question “On a scale of 1-10, how upset are you that
Zayn left One Direction?” and computed sample means and sample standard deviations from
each population.

3. Chester Cheetah is extremely concerned about quality control, and believes that the variance for the
average number of Hot Cheetos per bag is at least 15 cheetos, an unacceptable business practice.
You took a simple random sample of 71 bags of Hot Cheetos, and found s2 = 6.8 cheetos. Conduct
a hypothesis test at the α = .01 significance level to test Chester’s claim. Are his fears justified or
unfounded?

4. You are the chief statistician for the Lakers, and the general manager has narrowed his draft pick
down to two players, Player A and Player B. After taking a simple random sample of 15 of player
A’s games, you found that he scored an average of 18.3 points per game, with a sample variance of
19.7 points per game. After taking a random sample of 15 of player B’s games, you found that he
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scored 16 points per game, with a sample variance of 15.2 points per game. Let µA and σA
denote
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the mean points per game and variance in points per game for player A, and µB and σB denote the
same for player B.
(a) Test the null hypothesis that player A and player B have the same variance in points per game
against the alternative that player A’s variance is higher at the α = .05 significance level.

(b) Now, the general manager wants to know which player scores more on average. Based on your
answer to i), should we use a t-test with the pooled estimate s2p for equal variances, or a t-test
with ν for unequal variances?

(c) Based on your answer to b), test the null hypothesis that player A and player B score the same
number of points per game on average vs the two-sided alternative at the α = .05 significance
level.

(d) Based on the conclusions from a) and c), which player do you think is the better selection?
Briefly explain your answer.