# Question 3 A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 85 items, the defect…

**Question 3**

A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 85 items, the defect rate is 5.9% but the manager claims that this is only a sample fluctuation and production is not really out of control. At the 0.01 level of significance, test the manager’s claim.

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

(b) Calculate the value of the test statistic for this test.

(c) Determine the critical region(s) for this test.

(d) State the conclusion of this test. Give a reason for your answer.

**Question 4 **

The table below shows the age and favourite type of music of 668 randomly selected people.

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