3. Assume a normal distribution and use a hypothesis test to test the given clai

Question

3. Assume a normal distribution and use a hypothesis test to test the given claim. According to city reports, it was found that the mean age of the prison population in the city was 26 years. Marc wants to test the claim that the mean age of the prison population in his city is less than 26 years. He obtains a random sample of 25 prisoners, and finds a mean age of 24.4 years and a standard deviation of 9.2 years. At a significance level of 0.05, what should his conclusion be? Note: The p-value = 0.1966

A)Do not reject the null hypothesis. There is not sufficient evidence that the mean age is less than 26 years

B)Reject the null hypothesis. The evidence suggests that the mean age is less than 26 years.

C)There is not enough information to perform the test.

D)Do not reject the null hypothesis. There is not sufficient evidence that the mean age is less than 24.4 years

E)Reject the null hypothesis. There is sufficient evidence that the mean age is less than 24.4 years.

Explanation / Answer

Set Up Hypothesis
Null, H0: U=26
Alternate, H1: U<26
Test Statistic
Population Mean(U)=26
Sample X(Mean)=24.4
Standard Deviation(S.D)=9.2
Number (n)=25
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =24.4-26/(9.2/Sqrt(25))
to =-0.87
| to | =0.87
Critical Value
The Value of |t | with n-1 = 24 d.f is 1.711
We got |to| =0.87 & | t | =1.711
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Left Tail -Ha : ( P < -0.8696 ) = 0.19658
Hence Value of P0.05 < 0.19658,Here We Do not Reject Ho

A)Do not reject the null hypothesis. There is not sufficient evidence that the mean age is less than 26 years

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