Question

For the following experiments/questions, pick the most appropriate statistical test. You have the following statistical tests as choices: some may be used more than once, others not at all. Assume homogeneity of variance (where applicable) and the validity of parametric tests (where applicable), unless something is directly stated (e.g., “the data are not at all normal”) or otherwise indicated (viz., by the inspection of the data) which would indicate a strong and obvious violation of an assumption. This means you must inspect the data for violations of all assumptions. Please simply write the letter for the test as your answer. [You can, but need not, add an explanation.] A: one sample z-test B: one-sample t-test C: t-test for the difference between means for two related samples D: t-test for the difference between means for two independent samples with homogeneity of variance E: t-test for the difference between means for two independent samples with heterogeneity of variance F: Wilcoxon test G: Mann-Whitney test H: a one sample z-test for proportions (or a chi-square goodness of fit) I: chi-square goodness of fit only (where a one sample z-test of proportions is not appropriate) J: a two sample z-test for the difference between proportions (or a chi-square test of independence) K: chi-square test of independence only (where a two sample z-test for proportions is not appropriate.) L: ANOVA

1. I want to know if Californians are better swimmers than non-Californians. I measure ability to swim by timing how long it takes to swim 100 meters.

2. Gigi is a waiter at an Italian restaurant and wants to know if men or women tip her more money. She also wonders if smiling while serving them also affects her tip. Thus, at some tables she smiles and at the other tables she does not smile.

3. Emily wants to know if horses are attracted to a specific type of food. She gets 25 different horses and provides them with a choice of carrots, sugar cubes, hay, or apples. She then records which the horse eats first.

4. An experimenter is interested in looking at the impact of weight gain during students’ freshman year at college on the students’ happiness. The experimenter compared students who gained weight (15 pounds or more) during their freshman year with students who did not gain weight. It is safe to assume that the level of happiness can be treated as if it is interval in scale. Here is the data. Gained weight: 8 5 6 9 7 7 6 7 8 Did not gain weight 2 3 4 4 6 5 5 3 4 2 4 4 3 5 6 5 4 3

5. In a study of 3,401 Allergy Research Patients from five different allergy clinics throughout the Greater Los Angeles, the patients were asked if they preferred appointments in the morning or the evening. Do patients from different clinics show a difference in preference?

6. Grant is testing to see if people see more than 10 movies per year. He gets a sample of four people. It is known that the population distribution is normal, and it is known what the population standard deviation is.

7. An experiment was conducted to compare four drugs for minimizing migraine headaches. Two hundred people suffering from migraines were divided into four groups of fifty people each – one group per drug. After using the drug, the people were asked how much pain they were still feeling. Do a hypothesis test to see if drug type affects headache. (Assume pain is interval.) 8. Donna is testing to see if going to the beach to study for a test affects test score. The data are below Go to Beach 145 150 142 150 72 68 147 130 65 62 Doesn’t go to Beach 54 135 126 58 141 67 69 132 59 126

8.         Donna is testing to see if going to the beach to study for a test affects test score. The data are below

            Go to Beach                                145       150       142       150       72         68         147       130       65         62        

            Doesn’t go to Beach                     54         135       126       58         141       67         69         132       59         126      

Answer 1

Answer # 1)

There are two groups of siwmmers: californian and non-californian. They are being compared to see who is fasted

thsi would be 2 independent samples T tes. Answer choice D is correct. The variable being used is interval scale.

Answer # 2)

Here the effect of gender and smile on the amount of tip is being analysed

The two variables gender and simle are categorical factors and the amount of tip is ratio scale here

Hence one can make use of ANOVA. Hence answer choice L is correct

Answer # 3)

There are two factors here: type of food (categorical) and which of the food is most preferred by horses, we deal with proprotions here and hence one sample Z test can best serve the purpose here. Answer choice H is correct

Answer# 4)

Here again happiness is a dependent factor on weight gain, There are two groups: those who gained weight and those who didnot gain weight, their happiness is being compared in form of interval scale. Hence option D of 2 indepedennt sample T test fits in this scenario