2. A polling group wishes to compare the point of view of Democrats and Republicans, ignoring those who do not express a party affiliation in terms of their positions regarding the siting of a medical marijuana dispensary. Among the 290 self-declared Democrats, 195 indicate support having medical marijuana dispensaries in the city, compared to120 of the 190 self-declared Republicans. State and test the hypothesis of no difference in the proportion of Democrats and Republicans who support having marijuana dispensaries in Boston using the .05 level of significance.
3. Research conducted at the Indiana University School of Medicine has suggested that playing video games with violent themes can have an impact on the gamer’s brain activity. Based on MRI scans, the researchers noticed significant brain activity in adolescents who played violent video games for a half-hour period. This, however, begs the question of whether it was the game playing or the violent content that made the difference. To find out, a new research team has a group of 8 volunteer teenagers each play a violent video game on one day and a nonviolent video game on another day. Here are the brain activity scores (the higher the number, the greater the stimulation) for the eight subjects under the two conditions:
Subject    Violent game    Nonviolent game
1                           9                      7
2                           7                      7
3                           10                     8
4                            6                      6
5                            7                      5
6                            6                      7
7                            8                      6
8                            9                      7
Assess the impact of violent content by testing the difference between the two conditions with a .05 level of significance.
4. A school psychologist interviews a sample of middle school students about a variety of issues, including bullying. Of the 200 boys surveyed, 31% reported having been bullied during the previous 12 months. Of the 216 girls interviewed, 25% reported having been the victim of bullying over the same time frame. Based on these sample results and using the .05 level of significance, what can be inferred generally about gender differences in victimization among middle school students?
5. Given recent events, a sample of Democrats and Republicans were surveyed concerning their opinions regarding police use of force. A total of 500 Democrats and 400 Republicans were surveyed. 350 Democrats and 225 Republicans stated that they believed police used excessive force more often than they should. Test whether there is a difference in proportions of Democrats and Republicans that believe the police use excessive force. State and test the null and research hypotheses using the .05 level of significance.
6. Who tends to be the gym rats, men or women? A researcher studying sports, exercise and fitness collects data on the extent to which college students use the gym, and wants to see if there are gender differences in frequency of working out. Rather than survey students who might give an inflated response (the so-called social desirability effect), she is able to access ID card sign-in records for a random sample of 100 students. Summary statistics on frequency of gym use over a two-week time period are as follows:
                           Males          Females
Sample size             55                45
Mean                        6.7               6.2
Standard Deviation 2.5             2.2
Using the .05 level of significance, test for sex differences in gym use 6. A health researcher wishes to test for gender differences in age of onset among smokers. He surveys a group of adult smokers concerning the age when they first started smoking on a regular basis. The results are as follows:
                                  Male          Female
N                                    68                76
Mean                            14.2             13.7
Standard Deviation       2.1                2.4
7. The principal of a large high school near Boston was interested in whether obesity was related to academic performance. She drew and sample of 40 honors students and 75 others (roughly proportionate the numbers of such students in the school), and determined their BMI scores, obtaining the summary results shown in the table below. State and test (using a .05 significance level) the relevant hypotheses concerning differences in BMI scores between honors students and the rest, and interpret the results.
                                  Honors          Non-honors
Sample size                      40                   75
Mean                              29.4                28.2
Standard Deviation         22.1                19.8

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