With coating C, the number of times a drill bit can be used before it must be re

Question

With coating C, the number of times a drill bit can be used before it must be replaced has mean, = 237.5, and standard deviation, = 7.1. A new coating, N, is claimed to produce a higher mean and it is desired to test this claim statistically . In a random sample of n=36 bits with the new coating, = 240.1 and s = 6.24.

(a) Define a parameter to be used in determining the hypotheses for this testing situation and state the null and alternative hypotheses in terms of this parameter.

(b) With = .01, what conclusion would be reached? State your conclusion in the terminology of this example; not just reject some hypothesis or do not reject a hypothesis.

(c) For the test in part (b), bound its p-value.

(d) How large of a sample is needed so that for the test in part (b), (242) = .05? Hint: Because is unknown for coating N, you may use its estimate and you may round to two-decimal places.

(e) Based on your answer to part (d), for the test in part (b), i.e., with n=36, is (242) < .05, (242) = .05, or (242) > .05?

Explanation / Answer

(a) We can use mean (µ) as a paramter to determine the hypothesis.

H0: µ < µ0 , Population mean is less than 237.5

H1: µ > µ0 , Population mean is greater than 237.5

(b) z = (240.1 - 237.5) /(7.1/36)

= 2.19

It is a one-tailed test. Critical value for one tailed test at 0.01 level of significance is 2.33

2.19 < 2.33. Hence, we cannot reject the Null hypothesis. Which means that the new coating does not produce a higher mean.

c) P-value = 0.9857

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