Consider the hypothesis test given by Hop05 H1p

Consider the hypothesis test given by

Ho:p=0.5

H1:p<0.5

In a random sample of 225 subjects, the sample proportion is found to be p=0.51 .

(a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(b) Determine the p-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.

(c) Is there sufficient evidence to justify the rejection of Ho at the a=0.01 level? Explain.

Solution

(a) test statistic:

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

=(0.51-0.5)/sqrt(0.5*0.5/225)

=0.3

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(b) It is a left-tailed test.

So the p-value= P(Z<0.3) =0.6179 (from standard normal table)

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(c) Since the p-value is larger than 0.01, we do not reject Ho.

there is not sufficient evidence to justify the rejection of Ho