Question

A politician running for public office believes there should be tougher treatment for convicted criminals. For example, she believes that convicted embezzlers spend a mean of less than two years in prison. A random sample of 200 convicted embezzlers has a mean prison stay of 1.85 years with a standard deviation of .79 years. Using the p-value to make your decision, does the data support the politician’s belief at the .01 level of significance?

Answer 1

Ans : At 0.01 levle of significance there is not sufficient evidence to support the politician’s belief that convicted embezzlers spend a mean of less than two years in prison.

###################Explanation###################

Here we want to test the politician’s belief that convicted embezzlers spend a mean of less than two years in prison.

Let be the mean years spend in prison by convicted.

Therefore the hypothesis will be

The null hypothesis is given as

i.e mean years spend in prison by convicted is not different than 2 years.

i.e conviced spend a mean of less than two years in prison.

A random sample of 200 convicted embezzlers has a mean prison stay of 1.85 years with a standard deviation of .79 years.

Hence from random sample of size n=200

sample mean = 1.85

and standard deviation s= 0.79

The test statistic given as

=  -2.685215

Here the degree of freedom is given as

df= n-1

= 199

Obataining the p-value

P[t₁₉₉< -2.685215] = P[t₁₉₉ >2.685215]= 0.003929988

Rounding off

p-value = 0.004

At 0 .01 level of significance

Since p-value > 0.01

we failed to reject the null hypothesis.

Hence there is not sufficient evidence to support the politician’s belief that convicted embezzlers spend a mean of less than two years in prison.