Question

Deep hole drilling is a family of drilling processes used when the ratio of hole depth to hole diameter exceeds 10. Successful deep hole drilling depends on the satisfactory discharge of the drill chip. An experiment was conducted to investigate the performance of deep hole drilling when chip congestion exists. The length (in mm) of 50 drill chi8ps resulted in the following summary statistics: x = 81.2 mm, s = 50.2 mm . Conduct a test to determine whether the true mean drill chip length, μ, differs from 75 mm. Use a significance level of α = 0.01

Answer 1

The null and alternative hypothesis is ,

The test is two tailed test.

Since , the population standard deviation is unknown.

Therefore , use t-distribution.

Now , df=degrees of freedom=n-1=50-1=49

The critical values are , ; The Excel function is , =TINV(0.01,49)

The test statistic is ,

Decision : Here , the value of the test statistic does not lies in the rejection region.

Therefore , fail to reject Ho.

Conclusion : There is not sufficient evidence to support the claim that the true mean drill chip length differs from 75 mm.