Question

An automobile assembly line operation has a scheduled mean completion time, μ, of 13.5 minutes. The standard deviation of completion times is 1.4 minutes. It is claimed that, under new management, the mean completion time has decreased. To test this claim, a random sample of 26 completion times under new management was taken. The sample had a mean of 13.2 minutes. Assume that the population is normally distributed. Can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? Assume that the standard deviation of completion times has not changed.

Perform a one-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table.

The null hypothesis:	H0:
The alternative hypothesis:	H1:
The type of test statistic:	(Choose one)ZtChi squareF
The value of the test statistic: (Round to at least three decimal places.)
The critical value at the 0.05 level of significance: (Round to at least three decimal places.)
Can we support the claim that the mean completion time has decreased under new management?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 13.5
Alternative Hypothesis, Ha: μ < 13.5

This is a single mean z test

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (13.2 - 13.5)/(1.4/sqrt(26))
z = -1.093

Rejection Region
This is left tailed test, for α = 0.05
Critical value of z is -1.645.
Hence reject H0 if z < -1.645
, fail to reject null hypothesis.

we cannot support the claim that the mean completion time has decreased under new management