Here are the answers to exam 1. For some of the questions, I have provided explanatory material in regular type, and the answer in **bold**; all you need to write down is the answer. If you don't understand why your answer was wrong, you may e-mail me, talk to me before or after class, or set up a time to talk to me in my office. The exam was worth 15 points, so each question was worth 0.75 points. The class average was 12.3 points

**1. **One nominal variable (mounting from left or right), null hypothesis is 50% left and 50% right, total sample size (169) is less than 1000: **exact test of goodness-of-fit**

**2. **Two nominal variables (men vs. women, injury type), null hypothesis is same proportions of injuries in men and women, total sample size (294+267=561) is less than 1000: **Fisher's exact test of independence**

**3. **One measurement variable (wingspan/height ratio), null hypothesis is a theoretical expectation (ratio=1): **One-sample t-test**

**4. **One nominal variable (pit bull vs. German shepherd), one measurement variable (number of barks in 15 minutes), null hypothesis is the mean number of barks in 15 minutes is equal for the two dog types: **two-sample t-test**; one-way anova would also be acceptable if you see a question like this on future exams

**5. **standard deviation is largest, and standard error is smallest

**6. **I was thinking the obvious analysis was a test of independence, for which the null hypothesis would be that **the proportion of right-handed people with clockwise swirls equals the proportion of left-handed people with clockwise swirls.** However, if you were thinking of a repeated G-test of goodness-of-fit, one null hypothesis would be that the **proportion of clockwise swirls equals the proportion of counterclockwise swirls**.

**7. ****...of getting a deviation from the null hypothesis as big as you observed, or bigger, if the null hypothesis were true.**

**8. ****The data are highly skewed, with one or a few extreme values in one direction;** or **The data are something you wait for, like lifespan, and you don't want to wait until the end.** Either answer is acceptable; you don't get extra credit for putting down both.

**9. **Two nominal variables, cilantro soapy vs. not soapy, men vs. women; null hypothesis is same proportion of soapy taste in men and women; total sample size (156+212+620+576=1564) greater than 1000: **chi-square test of independence** or **G-test of independence**. You got points off if you said "chi-square or G-test of independence"; you have to pick only one. You could have kept the data from the three days separate, so I also accepted **Cochran-Mantel-Haenszel test**.

**10. ****A balanced design reduces the effects of heteroscedasticity** was the answer I was looking for, although I also accepted **A balanced design increases your power**. Note that an unbalanced design does not *cause* heteroscedasticity, it just makes the effects of heteroscedasticity worse, *if* there's heteroscedasticity.

**11. **One nominal variable (TV vs. no TV), one measurement variable (weight): **two-sample t-test**. One-way anova will also be correct if you see a question like this on future exams.

**12. ****Standard deviation would show you which group of rats had more variation of individual rat weights.**

**13. **Three nominal variables (pheromone vs. light, stinkbug vs. ladybug, 21 yards), null hypothesis is no difference in proportion of stinkbugs between pheromone and light trap at each yard: **Cochran-Mantel-Haenszel test**

**14. ****Size: ranked variable; tastiness: measurement variable.**

**15. **Two nominal variables (normal vs. tiny wings, 26 crosses), null hypothesis is 75% normal and 25% tiny wings in each cross: **repeated G-test of goodness-of-fit**

**16. **Two nominal variables (singing vs. not singing, warts vs. no warts), null hypothesis is the same proportion of singers and non-singers have warts, total sample size 200: **Fisher's exact test.** Note: I made this up, I don't really think singing to your warts will work. If you want to try it anyway, please don't sing in class.

**17. **Two nominal variables (MUNK17 vs. control, live vs. dead cells), null hypothesis is the same proportion of live cells in MUNK17 and control cells, total sample size (886+432+910+684)=2912) is greater than 1000: **chi-square test of independence** or **G-test of independence**.

**18. **One nominal variable (quadrant), null hypothesis is equal proportion in each quadrant, total sample size (75) is less than 1000: **Exact test of goodness-of-fit.**

**19. ****Tomato variety: nominal; Amount of coffee: measurement; Number of tomatoes per plant: measurement.**

**20. ****Effect size.** The question says you want a power of 0.8, so you already know that beta is 0.2; you got points off for saying you needed effect size AND beta. There's no measurement variable, so you got points off if you said you needed standard deviation.

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This page was last revised October 8, 2014. Its URL is http: //udel.edu/~mcdonald/statexam1answers.html