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 0.8 points.

**1. **two nominal variables (hair whorl direction, sexual preference), null hypothesis is the same proportion of clockwise vs. counterclockwise whorls in each preference, total sample size is less than 1000: **Fisher's exact test of independence**. (This kind of research has actually been done, and the first study really was crappy, although as far as I know none of the studies have included bisexual men.)

**2. **One nominal variables (music vs. no music), one measurement variable (time to fly home), null hypothesis is same mean time to arrive home with or without music: **Student's two-sample t-test**; one-way anova would also be acceptable if you see a question like this on future exams. You got points off if you just said "t-test"; you need to specify whether it's a one-sample or two-sample t-test.

**3. **Two nominal variables (experienced or inexperienced male, mated or unmated); null hypothesis is the proportion mated is the same for experienced and inexperienced males; total sample size (240) is less than 1000: **Fisher's exact test of independence**. Here's a picture I took of dung beetles a year ago.

**4. **Experienced males are marked with red dots, while inexperienced males are marked with blue dots, so **dot color is a possible confounding variable**; maybe the females have a preference for one color over the other. You could control this by **marking the males with something that the females can't detect**, such as dots that reflect differently at wavelengths that beetles can't see. You got points off if you correctly identified the confounding variable but didn't say how to control it; be sure to read the questions carefully and answer all parts. (Bird researchers, who use colored leg bands to mark individual birds in the wild, have actually found that the color of the leg band affects mating success; I don't know if similar problems have been found in insect studies, but it seems possible.)

**5. **One measurement variable (distance moved), null hypothesis is that the mean distance is zero: **Student's one-sample t-test.**

**6. ****glasses vs. no glasses (nominal), sex of housefly (nominal), position of fly in vomit string (ranked)**. (I'd be very surprised if frogs actually vomit in such an orderly fashion, but it's hard to think of biological ranked variables.)

**7. ****Dear second-best friend: because you analyzed four data sets, the chance of one of the P-values being less than 0.05, if the null is actually true, is much greater than 0.05. Basically, it's as if you said "If it's true that I have magic powers, I can draw a red ace from a deck of cards," then you kept drawing cards until the fourth card was a red ace. You should have either picked a sample size ahead of time and stuck with it, or used a statistical test that adjusts for the fact that you analyzed the data four times. But you're not necessarily evil, you just don't know as much about statistics as I do. Do you want to get together for lunch next week?**.

**8. ****Pheromone trap or light trap (nominal), ladybug or stink bug (nominal), which yard the traps are in (nominal).**

**9. ** One nominal variable (seed vs. feces), null hypothesis is that the beetle buries the seed in half of the trials, total sample size is greater than 1000: **chi-square or G-test of goodness-of-fit**. I'm not making up these feces-imitating seeds, click on the link for the remarkable story, including a video.

**10. ****Singing or no singing (nominal), wart or no wart (nominal), the group of patients studied by each individual dermatologist (nominal); null hypothesis is that the mean difference in proportion of warts in singing vs. no singing people is zero across all groups of patients: Cochran-Mantel-Haenszel test. **Note that the question says you count the number of people with warts (and could then figure out the number without warts); the question did *not* say that you count the number of warts on each person, which would have been a measurement variable. Also note that any time you repeat an experiment at different times, different places, or with different investigators or different groups of subjects, the identity of the repeated experiments is a nominal variable. It's important to treat it as a nominal variable because the experiment could give different results with different days, locations, or investigators. Also also note that I made this experiment 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.

**11. **One nominal variable (TV vs. no TV), one measurement variable (weight): **Student's two-sample t-test**. One-way anova will also be correct if you see a question like this on future exams.

**12. **Two nominal variables, cilantro soapy or not soapy, country; null hypothesis is same proportion of soapy taste in people from different countries; total sample size (32+27+19+42+37=157) less than 1000: **Fisher's exact test of independence**.

**13. **One nominal variable (right or left), one measurement variable (mating time): **Student's two-sample t-test**. One-way anova will also be correct if you see a question like this on future exams.

**14. **Two nominal variables (east or west half of tank, magnetic shielding on or off), null hypothesis is equal proportions of salmon in the east half when shielded vs. not shielded, total sample size less than 1000: **Fisher's exact test.** Note that when a possible answer is a pun, it's not *always* the correct answer, so be careful on future questions involving fish, tea, or G-spots.

**15. ****Alpha (also known as critical value); beta or power; effect size.** Note that you shouldn't put down *both* beta and power, as they're just two different ways of measuring the same thing (power is 1 minus beta). Also note that you don't need an estimate of the standard deviation, since there's no measurement variable in this experiment.

**16. ** **Amount of coffee (measurement), number of tomatoes (measurement), variety of tomato (nominal).** The amount of coffee is a measurement variable because there are 8 different values for the amount, from 0 to 70 ml per day in increments of 10.

**17. ****...of getting a deviation from the null hypothesis as big as you observed, or bigger, if the null hypothesis were true."**. Note that a P-value of 0.04 definitely does *not* mean the probability that the null hypothesis is true. This is a common misconception that is very wrong. I'm not real big on memorization, but you might as well memorize the definition of P-value; you'll probably see a question requiring you to know it on every exam.

**18. ****A higher standard deviation of the mean growth rate near the road means that there is greater variation among growth rates of individual trees near the road; in other words, the observations are more spread out.** Note that a larger standard deviation does *not* result from a smaller sample size; that's true for standard error, not standard deviation.

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This page was last revised October 12, 2016. Its URL is http: //udel.edu/~mcdonald/statexam1answers.html