Question

A supervisor notes an increase in backlogs when one station’s productivity is different from other stations. He discovered that the scientist who developed the process assumed the amount of time to complete a part of the process is normally distributed with a mean of 130 seconds and a standard deviation of 15 seconds. He is satisfied that the process time is normally distributed with a standard deviation of 15 seconds but he is unsure about the mean time. In order to examine the problem he measures the time of 100 assemblies. The mean of these times was calculated to be 126.8 seconds.

A. Can the supervisor conclude at the 5% significance level that the assumption that the mean assembly time if 130 seconds is incorrect

B. State null and alternative hypothesis that best tests hypothesis of interest. 1-tailed or a 2-tailed test?

C. Carry out test. State whether you reject or fail to reject the null hypothesis. Indicate whether you are using “t” or “z” and use precise critical value.

Answer 1

A.

From the workings in B and C, it is clear that the supervisor can conclude at the 5% significance level that the assumption that the mean assembly time if 130 seconds is incorrect.

B.

Null hypothesis H₀: The mean assembly time is 130 seconds.

Alternate hypothesis H₁: The mean assembly time is other than 130 seconds.

The test is 2-tailed test as the rejection region lies in both sides of the testing parameter.

C.

The sample size is 100 (large enough) and the population standard deviation is known. So the appropriate test that can be used is the Z-test.

Assumptions:

The assumptions for the test are

i) The samples are random and independent.

ii) The samples are drawn from normal populations.

The test statistic for the Z-test is

Substitute the values in the above test statistic.

The level of significance to be used is 5% and so the right and left critical values at this level of significnace are -1.96 and 1.96 respectively.

The test statistic falls outside the range of the critical values. (-2.13 < -1.96). So there is suffcient evidence against the null hypothesis and so we reject the null hypothesis.