A sample of 140 observations revealed that p 095 At the 002

A sample of 140 observations revealed that p = 0.95. At the 0.025 significance level, can the null hypothesis be rejected?

Solution

(a) Given a=0.025, the critical value is Z(0.025) = 1.96 (from standard normal table)

Reject H₀ and fail to rejectreject H₁ if z > 1.96

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(b)test statistic:

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

=(0.95-0.87)/sqrt(0.87*(1-0.87)/140)

=2.81

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(c)Reject H₀.