A production run of 500 items resulted in 29 defectives items.A defective item is coded as 1 and a good item as 0.The following is an output from Minitab.
Runs Test: Defects

Runs test for Defects

Runs above and below $\mathrm { K } = 0.058$

The observed number of runs $= 57$
The expected number of runs $= 55.636$
29 observations above K, 471 below
$\mathrm { P } -$ value $= 0.574$
Using $\alpha$=0.1, the conclusion is __________________.
A)successive items did not constitute a random sample.
B)reject the hypothesis that successive items constituted a random sample
C)do not reject the hypothesis that successive items constituted a random sample
D)reject the hypothesis that successive items constituted a random sample.
E)the distribution is binomial

Question

A production run of 500 items resulted in 29 defectives items.A defective item is coded as 1 and a good item as 0.The following is an output from Minitab. 
Runs Test: Defects

Runs test for Defects

Runs above and below $\mathrm { K } = 0.058$

The observed number of runs $= 57$
The expected number of runs $= 55.636$
29 observations above K, 471 below
$\mathrm { P } -$ value $= 0.574$
Using $\alpha$=0.1, the conclusion is __________________.
A)successive items did not constitute a random sample.
B)reject the hypothesis that successive items constituted a random sample
C)do not reject the hypothesis that successive items constituted a random sample
D)reject the hypothesis that successive items constituted a random sample.
E)the distribution is binomial

Quizplus · Accepted Answer

The runs test is used to determine if the occurrences of different values in a dataset are random or not. In this case, the values are either 0 (good item) or 1 (defective item).

The null hypothesis for the runs test is that the occurrences of the values are random. The alternative hypothesis is that they are not random.

The p-value for this test is 0.574 which is greater than the significance level of 0.1. Therefore, we fail to reject the null hypothesis and conclude that successive items did constitute a random sample. So, the best choice is C.

A Production Run of 500 Items Resulted in 29 Defectives K=0.058\mathrm { K } = 0.058K=0.058

A Production Run of 500 Items Resulted in 29 Defectives $\mathrm { K } = 0.058$