Consider the following hypothesis test. H0: p = 0.45 Ha: p ≠ 0.45 A sample of 200 provided a sample proportion p = 0.443.
(a) Compute the value of the test statistic.
(b) What is the p-value?
(c) At α = 0.05, what is your conclusion?
(d) What is the rejection rule using the critical value? What is your conclusion?
a)
Test statistics
z = (
- p) / sqrt ( p ( 1 - p) / n )
= ( 0.443 - 0.45) / Sqrt ( 0.45 * ( 1 - 0.45) / 200)
= -0.20
b)
For two tailed test,
p-value = 2 * P(Z < z)
= 2 * P(Z < -0.20)
= 2 * 0.4207
= 0.8414
c)
Since p-value > 0.05 level, fail to reject H0
d)
Critical values at 0.05 level = -1.96 , 1.96
Rejection rule = Reject H0 if | z | > 1.96
Since test statistics falls in non-rejection region, fail to reject H0
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