Consider the hypothesis test given by H0p05 H1p

Consider the hypothesis test given by
H₀:p=0.5

H₁:p<0.5
In a random sample of 225 subjects, the sample proportion is found to be p

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