Easy Talk phones have an electronic component that isproduced by WiredUp Inc. Under normal operations 8% of thesecomponents are defective. Every week, the production process istested by inspecting 10 of the new components produced. If 2 (or20%) or more are defective they shut down the production processfor further inspection. The null and alternative hypotheses of thetest are:
(null) H0 : π = 0.08
(alternative) Ha : π > 0.08
Where π is the proportion of components being producedthat are defective at the time of the test.
(a) What is the test statistic that is being used inthe test?
(b) What is the rejection region?
(c) Use an appropriate applet to determine theprobability they make a Type I Error and shut down the productionprocess unnecessarily.
(d) Suppose the machines producing the electroniccomponent get out of adjustment and 15% of the components beingproduced are defective. Use an appropriateapplet to find the probability the test will revealthat the machine is out ofadjustment.
(e) Now use a theory-based method (and not anapplet) to calculate the probability in (d)again.
(f) Both the calculations in (d) and (e) areapproximate. Which do you expect to be more accurate?Explain.
(g) Suppose the change from an 8% to 15% defectiverate is important for the company to detect. Briefly describe howthe company might modify the test, without increasing theprobability of a Type I Error, to increase the probability ofdetecting that the alternative hypothesis is true when thedefective rate is 15%.
