A plethora of measuring devices located in a universitys psy

A plethora of measuring devices located in a university\'s psychometrics lab is in need of calibration and maintenance. A certified calibration technician is called in to bring the instruments up to manufactures\' standards and promulgated tolerances. As the lead psychometrist, you are budge conscious and inquire to the technician as to the average on-site services cost or one unit. She claims that the mean cost for these & similar models is less than # 100 each. To test this claim, you randomly select the most recent maintenance records of five (5) of the lab\'s models and find that the mean service cost is # 75 with a standard deviation of #12.50. At an alpha level of 0.01, do you have enough evidence to support the technicians claim? Suppot the claim Reject the claim

Solution

Set Up Hypothesis
Null, H0: U=100
Alternate, H1: U<100
Test Statistic
Population Mean(U)=100
Sample X(Mean)=75
Standard Deviation(S.D)=12.5
Number (n)=5
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =75-100/(12.5/Sqrt(5))
to =-4.472
| to | =4.472
Critical Value
The Value of |t | with n-1 = 4 d.f is 3.747
We got |to| =4.472 & | t | =3.747
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Left Tail -Ha : ( P < -4.4721 ) = 0.00553
Hence Value of P0.01 > 0.00553,Here we Reject Ho

Support the cliam that, mea cost is less than 100