CHAPTER 15 #1
1. Parametric tests (such as t or ANOVA) differ from nonparametric tests (such as chi-square) primarily in terms of the assumptions they require and the data they use. Explain these differences.
3. In a study, a pair of faces is shown on a screen and the reasearchers record the amount of time the baby spends looking at each face. In a sample of n=40 infants, suppose that 26 spent the majority of their time looking at the more attractive face and only 14 spent the majority of the time looking at the unattractive face. Is this result significantly different from what would be expected if there were no preference between the two faces? Test with a=.05.
5. Research has demonstrated that people tend to be attracted to others who are similar to themselves. One study demonstrated that individual are disproportionately more likely to mary those with surnames that begin with the same letter as their own. The researchers began by looking at marriage records and recording the surname for each groom and the maiden name of each bride. From these records it is possible to calculate the probability of randomly matching a bride and a groom whos last names begin with the same letter. Suppose that this probability is only 6.5%. Next, a sample of n=200 married couples is selected and the number who shared the same last initial at the time they were married is counted. The resulting observed frequencies are as follows:
SAME INITIAL: 19
DIFFERENT INITIAL: 181
Do these data indicate that the number of couples with the same last initial is significantly different than would be expected if the couples were matched randomly? Test with a=.05.
6. Suppose the researcher from the previous problem repeated the study of married couples initials using twice as many participants and obtaining observed frequencies that exactly double the original values. The resulting data are as follows:
SAME INITIAL: 38
DIFFERENT INITIAL: 362
6A. Use a chi-square test to determine whether the number of couples with the same last initial is significantly different than would be expected if couples were matched randomly. Test with a=.05.
6B. You should find that the data lead to rejecting the null hypothesis. However, in problem 5 the decision twas fail to reject. How do you explain the fact that the two samples have the same proportions but lead to different conclusions?
9. The color red is often associated with anger and male dominance. Based on this observation, Hill and Barton monitored the outcome of four combat sports (Boxing, Tae Kwan Do, Greco-Roman wrestling, and freestyle wrestling) during the 2004 Olympic games and found that participants wearing red outfits won significantly more often than those wearing blue.
9A. In 50 wrestling matches involving red vs. blue, suppose that the red outfit won 31 times and lost 19 times. Is this result sufficient to conclude that red wins significantly more than would be expected by chance? Test at the a=.05 level of significance.
9B. In 100 matches, suppose red won 62 times and lost 38. Is this result sufficient to conclude that red wins significantly more than would be expected by chance? Again, use a=.05.
9C. Note that the winning percentage for red uniforms in part A is identical to the percentage in part B (31 out of 50 is 62%, and 62 out of 100 is 62%). Although the two samples have an identical winning percentage, one is significant and the other is not. Explain why the two samples lead to different conclusions.
12.Research has demonstrated strong gender differences in teenagers approaches to dealing with mental health issues. In a typical study, eighth-grade students are asked to report their willingness to use mental health services in the event they were experiencing emotional or other mental health problems. Typical data for a sample of n=150 students are shown in the following table.
WILLINGNESS TO USE MENTAL HEALTH SERVICES
Probably No Maybe Yes Total
Males 17 32 11 60
Females 13 43 34 90
Total 30 75 45
Do the date show a significant relationship between gender and willingness to seek mental health assistance? Test with a=.05.
13. Research indicates that playing a prosocial video game tends to increase prosocial behaviors. In a similar experiment, participants were assigned to play a prosocial, a violent (antisocial), or a neutral video game. Near the end of each session, the experimenter accidentally spilled a box of pencils on the floor and then recorded whether the participant stopped to help pick them up. The data are as follows:
Did Not Help: 3
Total, prosocial: 15
Did not Help: 8
Total, violent: 15
Did Not Help: 7
Total, neutral: 15
Did Not Help:18
Do the data indicate a significant relationship between the type of game played and helping behavior? Test with a=.05.