Question

1.   An automobile parts supplier owns a machine that produces a cylindrical engine part. This part is supposed to have an outside diameter of three inches. The technical staff feels that the mean diameter produced by the machine is off target. In order to verify this, a special study will randomly sample 40 parts produced by the machine. The 40 sampled parts will be measured, and if the results obtained cast a substantial amount of doubt on the hypothesis that the mean diameter equals the target value of three inches, the company will assign a problem-solving team to intensively search for the causes of the problem.

a. Formula the hypotheses so that the problem-solving team will be assigned when the null hypothesis is rejected.

b. A sample of 40 parts yields a sample mean diameter of 3.006 inches. Assume that the population standard deviation equals 0.016 inches. (1) Use the critical value approach to test H₀ versus H_a when α = 0.05. (2) Use the p-value approach to test H₀ versus H_a when α = 0.05.

Answer 1

Answer

(A) We have to test whether the mean is equal to 3 inches or off the target

Null hypothesis

Alternate hypothesis

(B) Given that population mean (mu) = 3, sample mean (x bar) = 3.006, population standard deviation (sigma) = 0.016 and sample size n = 40

z test statistic =

(1) Using critical value table for alpha level 0.05, we get z critical = -1.96 and + 1.96 (for two tailed hypothesis)

it is clear that z calculated is outside the range of -1.96 and +1.96, so we can reject the null hypothesis as the result is significant.

(2) using z distribution table with z value 2.37, check 2.3 in the left most column and 0.07 in the top row, then select the intersecting cell, we get

p value = 0.0178

p value is less than 0.05 significance level, again rejecting the null hypothesis.

So, we can conclude that the machine is off the target