Question

Victoria Snelgrove was a 21-year-old college student who was shot and killed with a police projectile after the Boston Red Sox beat the Yankees in the American League Championship Series. Following the incident, you take a random sample of 144 criminal justice students here at university and ask them to rate their level of outrage over police use of force in this case. On a scale from 1 to 10, respondents rate their outrage at 7.8. The average level of outrage for all Americans before the incident was known to be 7.0 with a standard deviation of 5. You hypothesize that the level of outrage will increase as a result. Using an a = .05, test the research hypothesis that the level of outrage is greater after this incident as it was before the incident (only of these tests is appropriate: one-tail OR two-tail, the other is wrong)

Answer 1

We have to test, H0: $\mu$ = 7 against H1: $\mu$ > 7, where, $\mu$ is the mean outrage rating given by the respondents.

The test is one sided (right tailed).

The test-statistic is given by, Z = $\frac{\overline{X} - \mu}{\sigma/\sqrt{n}}$ , where, $\overline{X}$ = 7.8, $\mu$ = 7, $\sigma$ = 5 and n = 144

Thus, Z = 1.92

Under H0, Z ~ N(0,1)

The p-value = P(Z > 1.92) = 1 - P(Z < 1.92) = 1 - $\Phi$ (1.92) = 1 - 0.9726 = 0.0274

Since, p-value < level of significance (0.05), we fail to reject the null hypothesis.

We conclude that the level of outrage is significantly higher after the accident as it was before the accident.