The results of given question's parts based on hypothesis testing.
a) Null and Alternative hypothesis
H₀ : p = 0.8
H₀ : p = 0.8 Hₐ : p < 0.8
b) test statistic (z value ) is Z = -2.25.
c) P- value ( Z꜀ ) is - 1.64
d) Rejected the null hypothesis.
We have given that
Sample size, n = 900
Hypothesis population proportion, p₀ = 0.80
Sample proportion , p-hat = 0.77
favourable cases, X = 693
significance level, α = 0.05
a) The following null and alternative hypothesis for population proportion needs to be tested :
H₀ : p = 0.8
Hₐ : p < 0.8
This is corresponding to a left tailed test for a z test for one population will used .
c) we have given that, Significance level is α=0.05 and the critical value for a left tailed test is Z꜀ = - 1.64
so, the rejection region for left tailed test R = { Z Z<- 1.64 }
b) Z- statistic value :
Z = (p-hat - p₀)/√p₀(1-p₀)/n
=> Z = ( 0.77 - 0.8 )/√0.8×0.2/900
=> Z = -2.25
d) Decision about Null hypothesis,
Since, it is observed that Z = - 2.25 < Z꜀ = - 1.645 it is then concluded that the null hypothesis is rejected. Reject the null hypothesis. There is not enough evidence to conclude that the percentage of infants who receive immunization s is less than 80%.
To learn more about Null hypothesis, refer:
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