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# ECON 15B Study Guide - Midterm Guide: Test Statistic, Standard Deviation, Repeated Measures DesignExam

Department
Economics
Course Code
ECON 15B
Professor
Paul Shirey
Study Guide
Midterm

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NAME: _________________________________ I.D.: _____________________________________
TEST THREE
PROBABILITY AND STATISTICS, ECON 15B
JULY 13, 2018
For the following experiments (1 4), state whether we should use A) a one-sample z test for means; B) a one-sample t-test for means;
C) a repeated measures t-test; D) an independent t-test (pooled samples); E) an independent t-test (un-pooled samples); F) a one sample z-
test for proportions; G) a two-sample z-test for the difference between proportions; or H) none of the above. Don’t assume that any
information about the population exists unless it is stated. Furthermore, it may be that in some cases a t-distribution and a z-distribution
are very similar. This does not mean that there are two acceptable answers. Pick the best answer.
1. Jo is testing to see if UCI students can sing “Twinkle, Twinkle, Little Star” faster than the average American (16.2 seconds). The
distribution of time is normally distributed. She gets a sample of three UCI students.
2. Can people run faster in the sun or in the shade? There are 1000 people who run in the sun and in the shade.
3. Bob wants to know if a greater percentage of men or women can pass a history test. There are 200 men and 200 women.
4. Zoe wants to know if UCI students drink more beer than the average American (28 gallons per year). She notes that individually,
UCI students either drink a lot of beer or no beer at all. She has a sample of twenty UCI students.
5 6. (Two questions twenty points) Let’s do a t-test. The average American attends 4.3 movies per year. Rose believes that UCI
students are not typical Americans. She takes a sample of six students and asks them how many movies they go to. The data are: 0, 8,
12, 12, 16, 24. Please calculate the test statistic, state the critical value, and come to a conclusion concerning UCI students’ attendance of
movies compared with the average American. Let α = .05. Let it be a two-tailed test.
7. If you underestimate sigma, the standard deviation of the population, the result is
a) the t-statistic being too small
b) the estimated standard error being too large
c) a smaller probability of Type I error
d) all of the above
e) none of the above
8. The t-distribution is more flattened out than the normal curve. What causes the t-distribution to be flattened out? (Be as clear and
precise, yet brief, as possible. The better the answer, the more the points.)
9. Why are related samples tests more powerful than independent samples tests?