Question

Assume that when victims are asked how well their needs were met by the criminal justice system on a scale of 1 (not met at all) to 5 (met completely), the average response is 3.24. In a study of 130 victims, Brewster (2001) found that the average response to how police officers met victims’ needs was 2.90 (standard deviation = 1.44). Perform a hypothesis test to determine if police officers respond less well to victims’ needs than the criminal justice system as a whole. Use a 0.05 level of statistical significance. What is the alternative hypothesis? H1: µ < 3.24 H1: µ >3.24 H1: µ < 2.90 H1: µ>2.90

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u > 3.24
Alternative hypothesis: u < 3.24

Note that these hypotheses constitute a one-tailed test.  

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.1263
DF = n - 1

D.F = 129
t = (x - u) / SE

t = - 2.692

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of - 2.692.

Thus the P-value in this analysis is 0.004.

Interpret results. Since the P-value (0.004) is less than the significance level (0.05), we have to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that police officers respond less well to victims’ needs than the criminal justice system as a whole.