Question

We want to validate the suspicion that the duration of the antibodies generated by exposure to COVID 19 has an average of no more than 180 days. 50 patients are monitored and the following result is obtained:

The result of the experiment shows that x = 184 days; s = 12.03 days

Calculate the probability of doing an error of type 2 if in reality:

u = 175 days

u = 182 days

Answer 1

(a) u = 175 days:

Sample Size, n = 50

Type I error rate, α = 0.05

True mean, μ = 175

Null Hypothesis mean, μ0 = 180

Standard Deviation, σ = 12.03

Type II error = 1 - [Φ(|μ−μ0|/σ/√n - z1−α)] = 1 - [|175 - 180|/12.03/√50 - 1.96] = 0.0976

(b) u = 182 days

Sample Size, n = 50

Type I error rate, α = 0.05

True mean, μ = 182

Null Hypothesis mean, μ0 = 180

Standard Deviation, σ = 12.03

Type II error = 1 - [Φ(|μ−μ0|/σ/√n - z1−α)] = 1 - [|182 - 180|/12.03/√50 - 1.96] = 0.6801