Question

Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. A study was then done to see if the mean time has increased in the new century.

A random sample of 26 first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was 3 years. Suppose that it is somehow known that the population standard deviation is 1.5 years.

Conduct a hypothesis test to determine if the mean length of jail time has increased. Assume the distribution of the jail times is approximately normal. Use a 1% level of significance.

a.) What is α? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

αα =

H0H0: μμ =

H1H1: μμ Select an answer > not = <  

The test is a Select an answer left-tailed right-tailed two-tailed  test

b.) Identify the Sampling Distribution you will use. What is the value of the test statistic?

The best sampling distribution to use is the Select an answer Student's t Normal  distribution.

The test statistic (z or t value) is =

c.) Find or estimate the P-value for the test.

The p-value is =

d.) Conclude the test.

Based on this we will Select an answer Reject Fail to reject  the null hypothesis.

Answer 1

a.) What is α? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

α = 0.01

we want to test that the mean time spent in jail by a first-time convicted burglar is increased from 2.5 years.
H0: μ = 2.5 years

H1: μ > 2.5 years  

b)

b.) Identify the Sampling Distribution you will use. What is the value of the test statistic?

The best sampling distribution to use is the Normal distribution.

because the population std deviation is known

The test statistic (z)  is = 1.7

P-value = ?

P-value = P(Z >z )

=P( Z > 1.7)

= 1- P(Z <1.7)

= 1 - 0.9554 ......... from normal table

= 0.0446

P-value = 0.0446

Reject Ho if P-value < level of significance = 0.01

Here P-value =0.0446 > 0.01

So we fail to reject Ho at a 1% level of significance.

we may conclude that the data do not provide sufficient evidence to support the claim that the mean length of jail time has increased.