a sample of 300 items was selected compute the pvalue and st

a sample of 300 items was selected. compute the p-value and state your conclusion for each of the following sample results. Use Alfa=.05

Ho: p is greater than or equal to .75

Ha: p is less than .75

A. pbar=.68

B. pbar= .72

C. pbar= .70

D. pbar= .77

It is a left-tailed test.

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A. pbar=.68

The test statisitc is

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

=(0.68-0.75)/sqrt(0.75*0.25/300)

=-2.8

So the p-valeu= P(Z<-2.8) = 0.0026 (from standard normal table)

Since the p-value is less than 0.05, we reject the null hypothesis.

So we can conclude that p is less than .75

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B. pbar= .72

The test statisitc is

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

=(0.72-0.75)/sqrt(0.75*0.25/300)

=-1.2

So the p-valeu= P(Z<-1.2) = 0.1151 (from standard normal table)

Since the p-value is larger than 0.05, we do not reject the null hypothesis.

So we can not conclude that p is less than .75

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C. pbar= .70

The test statisitc is

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

=(0.70-0.75)/sqrt(0.75*0.25/300)

=-2

So the p-valeu= P(Z<-2) = 0.0228 (from standard normal table)

Since the p-value is less than 0.05, we reject the null hypothesis.

So we can conclude that p is less than .75

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D. pbar= .77

The test statisitc is

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

=(0.77-0.75)/sqrt(0.75*0.25/300)

=0.8

So the p-valeu= P(Z<0.8) = 0.7881 (from standard normal table)

Since the p-value is larger than 0.05, we do not reject the null hypothesis.

So we can not conclude that p is less than .75