Answer:
Step-by-step explanation:
We would set up the hypothesis test.
For the null hypothesis,
p ≤ 0.05
For the alternative hypothesis,
p > 0.05
This is aright tailed test.
Considering the population proportion, probability of success, p = 0.05
q = probability of failure = 1 - p
q = 1 - 0.05 = 0.95
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 43
n = number of samples = 1000
p = 43/1000 = 0.043
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.043 - 0.05)/√(0.05 × 0.95)/400 = - 0.64
Since the test is a right tailed test, we would find the probability value for the area above the z score. It becomes
p = 1 - 0.26 = 0.74
Let us assume a significance level of 0.05
Since alpha, 0.05 < than the p value, 0.74, then we would fail to reject the null hypothesis. A type I error occurs when a true null hypothesis is rejected. A type 2 error occurs when a false null hypothesis is accepted.
A type 2 error could have been made in part A.
A type 2 error would be more serious because people will believe that the vaccine is very effective in preventing the flu when it is not. This can lead to more adults getting the flu.
