As a sociologist, you are interested in determining whether people who know many

Question

As a sociologist, you are interested in determining whether people who know many of their neighbors feel safer in their own neighborhood than people who know very few of their neighbors. So you administer a survey to 60 individuals who know many of their neighbors and 50 people who know very few of their neighbors. You find that, in these samples, those who know many of their neighbors have a mean score on a measure of how safe they feel in their own neighborhood of 87 (with a sample standard deviation of 10) while those who know very few of their neighbors have a mean score of 80 on the measure of how safe they feel in their own neighborhood (with a sample standard deviation of 15). Perform the appropriate hypothesis test to determine whether people who know many of their neighbors feel more safe in their own neighborhood than people who know very few of their neighbors, at alpha = .01. NOTE: The standard error for the difference between means in this example is 2.42. Be sure that you include all of the steps discussed in class (including stating your hypotheses) and show any calculations you perform. Do you reject or fail to reject the null hypothesis? What does this decision mean? (i.e. following your decision, I want you to state your conclusion in a complete sentence, e.g. if you decide to reject the null then you would state “we reject the null and conclude….”)

Explanation / Answer

H0: 1 - 2 = 0 i.e. (1 = 2)

H1: 1 - 2 > 0 i.e. (1 2)

Assuming population variances are equal, we would have to calculate pooled-variance t-Test

Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)

         = (60-1)*10^2+(50-1)*15^2/59+49

         = 5900+11025/108

         = 156.71

tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)

       =(87-80)-0/156.71(1/60+1/50)

       =7/2.397

       =2.92

tCRIT is +/-2.36 and hence reject the null hypothesis. Thus we conclude that people who know many of their neighbors feel more safe in their own neighborhood than people who know very few of their neighbors

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