Two different companies have applied to provide cabletelevision service in a certain

Chapter 8, Problem 11

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Two different companies have applied to provide cabletelevision service in a certain region. Let p denote theproportion of all potential subscribers who favor the firstcompany over the second. Consider testing H0: p 5 .5versus Ha: p .5 based on a random sample of 25 individuals.Let the test statistic X be the number in the sample who favor the first company and x represent theobserved value of X.a. Describe type I and II errors in the context of thisproblem situation.b. Suppose that x 5 6. Which values of X are at least ascontradictory to H0 as this one?c. What is the probability distribution of the test statisticX when H0 is true? Use it to compute the P-valuewhen x 5 6.d. If H0 is to be rejected when P-value # .044, computethe probability of a type II error when p 5 .4, againwhen p 5 .3, and also when p 5 .6 and p 5 .7. [Hint:P-value > .044 is equivalent to what inequalitiesinvolving x (see Example 8.4)?]e. Using the test procedure of (d), what would youconclude if 6 of the 25 queried favored company 1?