Question

QUESTION 3

(a) Consider the following hypothesis:

?0 ∶ ? ≤ 12.6

?1 ∶ ? > 12.6

A sample of 25 measurements yields a sample mean of 13.4. Assuming that the sample is drawn from a normal distribution with a known population standard deviation of 3.2.

(i) Use Z-test to determine the conclusion if ? = 0.10.

(ii) Use p-value test to determine the conclusion if ? = 0.10. [15 marks]

(b) A perfume factory wishes to ensure that an average of 16 ml of perfume is used to fill each bottle. In order to analyse the accuracy of the bottling process, he takes a random sample of 48 bottles. The mean weight of the sample is 15.8 ml. Assume that the population standard deviation is 0.8 ml.

(i) State the null and the alternative hypotheses for the test.

(ii) use the critical value approach to test the bottler's concern at ? = 0.05.

(Iii) make a recommendation to the bottler. [15 marks]

Answer 1