Question

The quality department at an electronics company has noted that, historically, 92% of the units of a specific product pass a test operation, 6% fail the test but are able to be repaired, and 2% fail the test and need to be scrapped. Due to recent process improvements, the quality department would like to test if the rates have changed. A recent sample of 500 parts revealed that 475 parts passed the test, 18 parts failed the test but were repairable, and 7 parts failed the test and were scrapped. (You may find it useful to reference the appropriate table: chi-square table or F table)

a. Choose the appropriate alternative hypothesis for the test. At least one of the pi (i = 1, 2, 3) differs from its hypothesized value. All pi (i = 1, 2, 3) values differ from its hypothesized value. b-1. Compute the value of the test statistic.

Answer 1

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Answer:

Part a) We have to test for :

All proportions are same to the hypothesized value

Vs

At least one the proportion is different from the hypothesized value.

Thus for first part a) first option is correct for alternative hypothesis.

Part b) Test statistic value.

formula for test statistic is :

              

Oi	Expected %	Ei	Oi2/Ei
475	92%	460	490.4891304
18	6%	30	10.8
7	2%	10	4.9
N=500			506.1891304

           

506.1891304 - 500 = 6.1891304

Test statistic = 6.1891

Look in chi square table in row of df = 2 and look for interval in which t = 6.1891

From the table we can see that for df = 2 p-value less than 0.05 but greater than 0.025