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
P-value $= 0.574$
The null hypothesis for a one-sample runs test is __________________.
A)successive items did not constitute a random sample.
B)successive items constituted a random sample
C)the proportion of defective items is 0.05
D)the proportion of defective items is 0.058
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
P-value $= 0.574$
The null hypothesis for a one-sample runs test is __________________.
A)successive items did not constitute a random sample.
B)successive items constituted a random sample
C)the proportion of defective items is 0.05
D)the proportion of defective items is 0.058
E)the distribution is binomial

Quizplus · Accepted Answer

The null hypothesis for a one-sample runs test is that successive items constitute a random sample, meaning that there is no pattern or trend in the data. The p-value of 0.574 is greater than the usual threshold of 0.05, so there is not enough evidence to reject the null hypothesis. Therefore, we can conclude that successive items in the production run did constitute a random sample.

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 $\mathrm { K } = 0.058$