Statistical inference using significance tests



Psych 318: Statistical inference using significance tests

1. A researcher is interested in citizens’ opinions about income redistribution in the United States. Participants in the researcher’s survey were asked whether they thought it is the government’s responsibility to reduce income differences between the rich and poor. What sort of test could you use to determine whether public opinion is not equally divided?

In the 1991 General Social Survey of 1227 adults, 591 people responded that it should be the government’s responsibility to reduce income differences. How would you carry out the test you listed above?

2. A political scientist has taken a look at the 2004 election results for twelve randomly selected US counties and notes that the correlation between percentage of votes for George Bush and the county population is -.35. What sort of test could you use to determine whether there is there a reliable relationship between county population and percentage votes for George W. Bush?

3. A study compared various treatments (cognitive behavioral treatment, intensive psychoanalytic therapy, self-help manual, group therapy) for young girls (12 – 14 years old) suffering from anorexia nervosa. The variable of interest was each participant’s rating (on a scale of 1 – 100) of her ability to maintain regular eating habits for the six weeks following the end of therapy.

a. What is the appropriate statistical test of the null hypothesis that there is no effect of treatment on girls’ confidence in their ability to maintain regular eating habits? ANOVA overall F test

b. What is the appropriate statistical test of the a priori null hypothesis that there is no difference between CBT and intensive psychoanalytic therapy? multiple comparison test – exactly which one depends on the entire set of a priori tests.

4. Suppose you have been told that a mean caloric intake of 1200 kcal per day is necessary for healthy growth in boys 10 – 12 years old. A recent study revealed that the daily caloric intake for a random sample of 30 boys who receive free lunches from various elementary schools in your region ranged from 700 to 1500 calories per day, with a mean of 1100 calories and a standard deviation of 200 calories. Is reasonable to conclude that mean daily caloric intake among low income boys is significantly below the recommended level? What test would you use to answer this question?

5. You have decided to compare the popularity of two sets of adjectives describing personality types. One set contains words with psychological connotations (e.g. “introverted” “depressed” “egocentric”), while the other set includes words that are generally not considered “psychological” (e.g. “quiet” “sad” “selfish”). Every participant in your study rates pairs of similar words, yielding an average “preference” score for each participant for “psychological words” and “not psychological words”. Your hypothesis is that psychology majors will show a stronger preference for words in the first set than in the second set. Which statistical test would be appropriate to test this hypothesis?

What if you were interested in whether psychology majors rate “psychological words” higher than engineering majors? Would you use the same test? Why or why not?

6. A graduate student in the psychology department has decided to compare the popularity of pecan, pumpkin, and cherry pies. He assumes that some people eat more of all kinds of pie than others do, so he decides to use a within-participants design. The dependent variable is the amount of each pie (in grams) eaten by each of the 9 participants. Of course order was randomized in order to counterbalance for order, but it was not considered a nuisance variable.

What type of analysis of variance test would be most appropriate to test the overall null hypothesis of no differences in popularity?

What sort of analysis would the grad student have to use in order to answer the specific question of whether pecan pie is more popular than pumpkin pie?

7. A researcher is interested in whether pie consumption is the same for each region of the country. She randomly samples 100 people from New England, 100 people from the deep south, 100 people from the American southwest, and 100 people from the northwest US and classifies them as to whether they have eaten pie not at all in the last month, once or twice in the last month, or more than twice in the last month. What sort of statistical analysis will she use to answer her question?

8. A researcher is interested in whether dessert preference is related to age. 400 shoppers at Fred Myers were randomly sampled and were asked whether they preferred cookies, cake, pie or ice cream as dessert. The surveyor also noted whether the person appeared to be a teenager, young adult, middle aged adult, or senior adult. What sort of analysis should the researcher use to test the null hypothesis that there is no relationship between the variables?

9. An educator is interested in whether WASL math scores are normally distributed. He takes a random sample of WASL math scores from several high schools across the state. What sort of analysis might he use to answer his question?

10. A researcher is interested in whether the effect of a person’s education on how easily persuaded the person is depends on the person’s gender. Persuadability is measured by “change in opinion” score. Subjects were males and females who had either only a high school education, some college, or a college degree. Is the researcher’s question one about main effects or interaction? What is the appropriate test of her question?

11. An intelligence test developer has created two versions of an intelligence test, but she wonders whether it is safe to assume that the variance of scores on each of the test will be equal. She obtains 100 people to take the test, and randomly assigns half to take version A and half to take version B. How can she analyze her data to answer her question?

12. Another intelligence test developer has created a shorter version of the standard IQ test and wants to make sure that the variance of her test is not significantly different from the standard test’s variance, which is 225. How can she design a study to examine her question? What will be the appropriate statistical test to use?

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