(Solved): A random survey of 75 death row inmates revealed that the mean length of time on death row is \( 17 ...

A random survey of 75 death row inmates revealed that the mean length of time on death row is \( 17.1 \) years with a standard deviation of \( 6.5 \) years. Conduct a hypothesis test to determine if the population mean time on death row could likely be 15 years. Part (a) Part (b) \( \operatorname{Part}(\mathrm{c}) \) Part (d) What symbol represents the random variable for this test? In words, define the random variable for this test. the proportion of time spent on death row for 75 inmates the amount of time spent on death row for 75 inmates the number of inmates on death row the standard deviation of time spent on death row for 75 inmates the mean time spent on death row for 75 inmates Part (f) Is the population standard deviation known? Yes No If so, what is it? (Enter your answer to one decimal place. If the standard deviation is Part (g) Calculate the following. (i) Enter your answer to one decimal place. \[ \bar{x}= \] (ii) Enter your answer to one decimal place. \[ s= \] (iii) Enter your answer as a whole number. Which test should be used? Normal test Student's t-test Part (0) State the distribution to use for the hypothesis test. (Enter your answer in the form z or tor where of is the degrees of freedom.) Part (j) Find the p-value. (Round your answer to four decimal places.) Part \( (k) \) At a pre-conceived \( \alpha=0.05 \), what do you determine for each of the following? (i) Decision: reject the null hypothesis do not reject the null hypothesis (ii) Reason for the decision: Since \( x> \) p-value, wo reject the null hypothesis. Since \( \alpha

p \)-value, we do not reject the null hypothesis. (iii) Conclusion (write out in a complete sentence). There is sufficient evidence to conclude that the mean fength of time on death row is not 15 years. There is not sufficient evidence to conclude that the mean length of time on death row is not 15 years.