A manufacturer makes ball bearings for a very precise mechan

A manufacturer makes ball bearings for a very precise mechanical application. The bearings are supposed to have a mean diameter of 1.150 cm. The customer\'s machines have been breaking down frequently, so it is suspected that the mean diameter is not equal to 1.150 cm. To test this, the customer takes a random sample of 28 bearings from a recent shipment of replacement bearings and finds that they have a mean diameter of 1.151 cm with a standard deviation of 0.0018 cm. Use a 0.01 significance level to test whether the bearings meet the stringent specifications. Based on your results, make a recommendation on whether the customer should continue to use this particular manufacturer, or find a new one.

Solution

Set Up Hypothesis
Null, H0: U=1.15
Alternate, H1: U!=1.15
Test Statistic
Population Mean(U)=1.15
Sample X(Mean)=1.151
Standard Deviation(S.D)=0.0018
Number (n)=28
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =1.151-1.15/(0.0018/Sqrt(27))
to =2.94
| to | =2.94
Critical Value
The Value of |t | with n-1 = 27 d.f is 2.771
We got |to| =2.94 & | t | =2.771
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != 2.9397 ) = 0.0067
Hence Value of P0.01 > 0.0067,Here we Reject Ho

it is suspected that the mean diameter is not equal to 1.150 cm, it should  find a new one