Question

The quality department at an electronics company has noted that, historically, 94% of the units of a specific product pass a test operation, 4% 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 479 parts passed the test, 16 parts failed the test but were repairable, and 5 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. (Round the intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) Test statistic b-2. Find the p-value. p-value Picture 0.10 0.05 Picture p-value < 0.10 0.025 Picture p-value < 0.05 0.01 Picture p-value < 0.025 p-value < 0.01 c-1. At the 5% significance level, what is your conclusion? H0 and cannot conclude at the 5% significance level that at least one of the proportions have changed from the historical rates. c-2. Would your conclusion change at the 1% significance level? No Yes

Answer 1

The statistical software output for this problem is:

Hence,

a) At least one of the pi (i = 1, 2, 3) differs from its hypothesized value. Option A is correct.

b - 1) Test statistic = 3.472

b - 2) p-value > 0.10

c - 1) Fail to reject H0 and cannot conclude at the 5% significance level that at least one of the proportions have changed from the historical rates.

c - 2) No