Question

A sample sequence of 35 products is selected (in order) from an assembly line. Each product is examined and judged to be either acceptable or defective. A total of 26 of these products were found to be acceptable, and the other 9 were found to be defective. The number of runs was 7. The runs test is to be used at the 0.05 significance level to test for randomness. Find the value of the test statistic used in this test, and round it to 3 places after the decimal point (if necessary)

Answer 1

GIVEN:

Number of products

Number of acceptable products

Number of defective products

Number of runs

HYPOTHESIS:

The hypothesis is given by,

The given sequence is random.

The given sequence is not random.

LEVEL OF SIGNIFICANCE:

TEST STATISTIC:

The test statistic is,

which follows standard normal distribution

where

CRITICAL VALUE:

The z critical value at significance level is .

CALCULATION:

  

  

  

  

  

  

DECISION RULE:

CONCLUSION:

Since the calculated z test statistic (-3.342) is less than the z critical value (-1.96), we reject null hypothesis and conclude that the given sequence is not random.