Question

Forty-one small lots of experimental product were manufactured and tested for the occurrence of a particular indication that is attribute in nature yet causes rejection of the part. Thirty-one lots were made using one particular processing method, and ten lots were made using yet a second processing method. Each lot was equally sampled (n = 30) for the presence of this indication. In practice, optimal processing conditions show little or no occurrence of the indication. Method 1, involving the ten lots, was run before Method 2. Determine, at the 0.05 level of significance, whether there is a difference in the proportion of reject product between the two methods. (Use Method 1 - Method 2.)

Methods	n	Number of Rejects
Method 1	300	6
Method 2	930	28

(a) Find z. (Give your answer correct to two decimal places.)

(ii) Find the p-value. (Give your answer correct to four decimal places.)

(b) State the appropriate conclusion.
Reject the null hypothesis, there is not significant evidence of a difference in proportions.
Reject the null hypothesis, there is significant evidence of a difference in proportions.    
Fail to reject the null hypothesis, there is significant evidence of a difference in proportions.
Fail to reject the null hypothesis, there is not significant evidence of a difference in proportions.

Answer 1

The statistical software output for this problem is:

Two sample proportion summary hypothesis test: P1 proportion of successes for population 1 P2: proportion of successes for population 2 P1-P2: Difference in proportions Ho:p1-p2 = 0 HA : p1-p2 # 0 Hypothesis test results Difference Count1 Total1 Count2 Total2 Sample Diff. Std. EZ-Stat P-value P1-P2 6 300 28 9 30-0.010107527 0.010885550.92852695 0,3531

Hence,

a) z = -0.93

ii) P-value = 0.3531

b) Fail to reject the null hypothesis, there is not significant evidence of a difference in proportions. Option D is correct.