Question

Hosiah is a pottery manufacturer. Past records of his production revealed that 10 % of output of coffee mugs were defective in some way and had to be sold off as rejects. Hosiah has recently introduced some new quality control procedures. In order to assess the effectiveness of these procedures, the line manager takes a random sample of 100 of the coffee mugs and examine them. He finds 7 defectives. On the basis of this evidence alone, has there been a significant improvement in the quality of the mugs? Use the 1% level of significance

Answer 1

Explanation:

We would set up the hypothesis test.

For the null hypothesis,

p = 0.1

For the alternative hypothesis,

p < 0.1

This is a left tailed test.

Considering the population proportion, probability of success, p = 0.1

q = probability of failure = 1 - p

q = 1 - 0.1 = 0.9

Considering the sample,

Sample proportion, p = x/n

Where

x = number of success = 7

n = number of samples = 100

p = 7/100 = 0.07

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.07 - 0.1)/√(0.1 × 0.9)/100 = - 1

To determine the probability value, we would look at the area below the z score on the normal distribution table.

From the normal distribution table, the area below the test z score in the left tail is 0.16

p = 0.16

Since alpha, 0.01 < than the p value, 0.16, then we would fail to reject the null hypothesis

Therefore, on the basis of this evidence alone, there has not been a significant improvement in the quality of the mugs