Your organization has a goal of 15 days for the average proc

Your organization has a goal of 15 days for the average processing of a purchase request (PR) from notification to final approval. They are only concerned if it takes longer than 15 days. A sample of 25 PRs produced a mean of 15.5 days and a standard deviation of 1.5 days. Test at the 10% level of significance whether they are meeting their goal. Select the correct answer out of each pair of choices. (Carry intermediate calculations to three decimal places.)

The tp is 1.711

The tp is 1.318

The tc is 1.667

The tc is 5.000

We would reject the null hypothesis

We would fail to reject the null hypothesis

We would conclude that the organization is meeting their goal.

We would conclude that the organization is not meeting their goal

Solution

Set Up Hypothesis
Null, H0: U<=15
Alternate, H1: U>15
Test Statistic
Population Mean(U)=15
Sample X(Mean)=15.5
Standard Deviation(S.D)=1.5
Number (n)=25
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =15.5-15/(1.5/Sqrt(24))
to =1.667
| to | =1.667
Critical Value
The Value of |t | with n-1 = 24 d.f is 1.318
We got |to| =1.667 & | t | =1.318
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Right Tail - Ha : ( P > 1.6667 ) = 0.05429
Hence Value of P0.1 > 0.05429,Here we Reject Ho

ANS:
to =1.667
We would reject the null hypothesis
We would conclude that the organization is meeting their goal