TEST THE HYPOTHESIS USING A THE CLASSICAL APPROACH AND B THE

TEST THE HYPOTHESIS USING A) THE CLASSICAL APPROACH AND B) THE P-VALUE APPROACH. BE SURE TO VERIFY THE REQUIREMENTS OF THE TEST

Ho: p=0.55 versus H1: p=0.55 n=150 x=78 alpha=0.1

Since the sample size is larger than 30, we can use normal distribution approximated.

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A) THE CLASSICAL APPROACH AND

The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(78/150-0.55)/sqrt(0.55*(1-0.55)/150)

=-0.74

It is a two-tailed test.

Given a=0.1, the critical values are Z(0.05) = -1.645 or 1.645 (from standard normal table)

The rejection regions are if Z<-1.645 or Z>1.645, we reject the null hypothesis.

Since Z=-0.74 is between -1.645 and 1.645, we do not reject the null hypothesis.

So we can conclude that p=0.55

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B) THE P-VALUE APPROACH.

The p-value= 2*P(Z<-0.74) = 0.4593 (from standard normal table)

Since the p-vaule is larger than 0.1, we do not reject the null hypothesis.

So we can conclude that p=0.55