Question

1. A researcher selected a random sample of 200 residents of Louisville, KY. The sample included 80 males and 120 females. The researcher asked the respondents to complete a survey that would measure the public trust in the police. This variable was coded 1 [low trust], 2 [average trust], and 3 [high trust]. Knowing that in each gender group 50% of the respondents acknowledged an average level of trust in the police and that 20 men and 20 women in the sample had a low level of trust in the police, (while the rest had a high level of trust in the police), determine if attitudes toward the police differ significantly by gender. In order to answer this question, you should also:                                                                                                                                [15 points]

                                                                                         

1. Identify correctly the independent and the dependent variable [remember that the IV / the comparison groups should be the columns of the table]
2. Create two contingency tables [Table 1 should include the observed and expected frequencies; Table 2 should include the percentages corresponding to various attitudes toward the police in each gender group (this would allow you to interpret the results)]
3. Formulate the null and the alternative hypotheses
4. Calculate the Chi-Square and test the null hypothesis after you calculate

Chi-Square -> C² = S[(fo – fe)²/fe]

5. Identify and record the critical Chi-square [see the table in your book] at the appropriate number of degrees of freedom and p<.05
6. Reach a statistical conclusion and substantively interpret your findings [Hint: inspect the percentages in Table 2 (the total for each column should be 100%)]

Answer 1

		Observed frequency  table
	Low	Average	High	Total
Male	20	40	20	80
Female	20	60	40	120
Total	40	100	60	200
	E1= RT*CT/GT= 80*44/200 =16
		Expected frequency  table
	Low	Average	High	Total
Male	16	40	24	80
Female	24	60	36	120
Total	40	100	60	200
H0: Attitudes toward the police differ insignificantly by gender.
H1: Attitudes toward the police differ significantly by gender.

	CALCULATION TABLE
	fo	fe	fo-fe	(fo-fe)2/fe
Male L	20	16	4	1
Female L	20	24	-4	0.66666667
Male A	40	40	0	0
Female A	60	60	0	0
Male H	20	24	-4	0.66666667
Female H	40	36	4	0.44444444
SUM =	200	200	0	2.77777778
df=(3-1)(2-1)=2			fo=OBSERVED
level=0.05OR 5%			fe= EXPECTED

Test statiatics Chi square =2.778

Crtical value of at 5% for 2df  = 5.99

and The P-Value =  0.24935

Statistical conclusion : Test statiatics Chi square =2.778 < 5.99

   or he P-Value (  0.24935) > 0.05

Fail to reject Ho

So we conclude that Attitudes toward the police differ insignificantly by gender.