Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.
-A researcher wants to check the claim that convicted burglars spend an average of 15.7 months in jail. She takes a random sample of 35 such cases from court files and finds that the mean time in jail is 13.7 months. Test whether the claim that the average jail time for convicted burglars is different from 15.7 months is supported or not supported. Assume that the population standard deviation is 7 months.
A)supported
B)not supported

Question

Quizplus · Accepted Answer

The test statistic is calculated as $ z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}} = \frac{13.7 - 15.7}{7/\sqrt{35}} \approx -1.69 $. The critical z-values for a two-tailed test at the 0.05 significance level are approximately ±1.96. Since -1.69 is within the range of -1.96 to 1.96, we fail to reject the null hypothesis. Therefore, the claim is not supported.

Conduct a Full Hypothesis Test and Determine If the Given