958 according to gartner inc the second largest share of the...

9.58. According to Gartner Inc., the second-largest share of the worldwide PC market is held by Hewlett-Packard with 21.7%. Suppose that a market researcher believes that Hewlett-Packard holds a higher share of the market in the western region of the United States. To verify this theory, he randomly selects 428 people who purchased a personal computer in the last month in the western region of the United States. Of these purchases, 104 were Hewlett-Packard computers. Using a 1% level of significance, test the market researcher's theory. If the market share is really 0.29 in the western region of the United States, what is the probability of making a Type II error?

Transcript

00:01 In this question we have been asked to test the claim as well as we need to find the value of probability such that here the null hypothesis can be written that p is equals to 0 .2 and then it is here 1 7.

00:14 Now we can say that alternate hypothesis will be that p is greater than 0 .217 and hence we can say that the value of n p and then it is here 1 minus p is here going to be 428 which is the value of sample size and then it is here 0 .217.

00:34 So it is the value of p assuming that the null hypothesis is true.

00:38 So this will be here equals to 72 point it is 72 and hence we can say that this is greater than 10.

00:46 So the sample size is large enough to approximate the sampling distribution of proportion as normal distribution and conduct one sample z test.

00:56 So it will be here 1 and then here it is sample.

01:00 Now here it is going to be z and then it will be here test.

01:04 Hence we can say that the sample is a random sample of 428 people and the sample size can be assumed to be less than or equals to 5 percent of the population size.

01:16 So all conditions for one sample z test are satisfied.

01:20 Therefore the standard error will be here equals to it is going to be under root of p and then here it is 1 minus p.

01:28 Now it will be here n.

01:29 So this is here going to be let us write under root of 0 .217 and then it will be here multiplied with 1 minus 0 .217 and now in the denominator it is 428.

01:42 So the value of standard error is here going to come around...

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