Question

A random survey of $75$death row inmates revealed that the mean length of time on death row is $17.4$years with a standard deviation of $6.3$years. If you were conducting a hypothesis test to determine if the population mean time on death row could likely be $15$years, what would the null and alternative hypotheses be?

a. $H_0$: __________

b. $H_a$: __________

Short answer

(a)$H_0:\mu =15$

(b)$H_a:\mu \ne 15$

Step-by-step solution

Part (a) Step 1: Given information

The average length of incarceration on death row is $17.4$years, with a standard deviation of $6.3$years, according to $17$death row convicts. The hypothesis test is to see if the average period spent on death row in the population is likely to be $15$years.

Part (a) Step 2: Explanation

$H_0:$The Null hypothesis: It is a statement of no difference between sample means or proportions or no difference between a sample mean or proportions and a population mean or proportion.

$H_0:\mu =15$

Part (b) Step 1: Given information

The average length of incarceration on death row is $17.4$years, with a standard deviation of $6.3$years, according to $17$death row convicts.

The hypothesis test is to see if the average period spent on death row in the population is likely to be $15$years.

Part (b) Step 2: Explanation

$H_a:$The alternative hypothesis: It is the claim about the population that is contradictory to $H_0$and what we conclude when we reject $H_0$.

$H_a:\mu \ne 15$