Applied Statistics and Probability for Engineers

314 CHAPTER 9 TESTS OF HYPOTHESES FOR A SINGLE SAMPLE

The first part of the output shows the power calculation based on the situation described in

Example 9-11, where the true proportion is really 0.03. The power calculation from Minitab

agrees with the results from Equation 9-35 in Example 9-11. The second part of the output

computes the sample size necessary to give a power of 0.9 (0.1) if p0.03. Again, the

results agree closely with those obtained from Equation 9-38. The final portion of the display

shows the sample size that would be required if p0.03 and the power requirement is re-

laxed to 0.75. Notice that the sample size of n561 is still quite large because the difference

between p0.05 and p0.03 is fairly small.

EXERCISES FOR SECTION 9-5

Power and Sample Size

Test for One Proportion

Testing proportion0.05 (versus 0.05)

Alpha0.05

Alternative Sample

Proportion Size Power

3.00E-02 200 0.3287

Power and Sample Size

Test for One Proportion

Testing proportion0.05 (versus 0.05)

Alpha0.05

Alternative Sample Target Actual

Proportion Size Power Power

3.00E-02 833 0.9000 0.9001

Power and Sample Size

Test for One Proportion

Testing proportion0.05 (versus 0.05)

Alpha0.05

Alternative Sample Target Actual

Proportion Size Power Power

3.00E-02 561 0.7500 0.7503

9-50. In a random sample of 85 automobile engine crank-

shaft bearings, 10 have a surface finish roughness that exceeds

the specifications. Does this data present strong evidence that

the proportion of crankshaft bearings exhibiting excess sur-

face roughness exceeds 0.10? State and test the appropriate

hypotheses using    0.05.

9-51. Continuation of Exercise 9-50.If it is really the

situation that p0.15, how likely is it that the test proce-

dure in Exercise 9-50 will not reject the null hypothesis? If

p0.15, how large would the sample size have to be for us

to have a probability of correctly rejecting the null hypothe-

sis of 0.9?

9-52. Reconsider the integrated circuits described in

Exercise 8-48.

(a) Use the data to test H 0 : p0.05 versus H 1 : p0.05. Use

 0.05.

(b) Find the P-value for the test.

Minitab will also perform power and sample size calculations for the one-sample Z-test on a

proportion. Output from Minitab for the engine controllers tested in Example 9-10 follows.

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