Question

25) A researcher is interested in investigating the power of his statistical test analyzing the success rate of increasing forced vital capacity (FVC) in children with asthma. Suppose the researcher conducted a z test for significance with a SRS of 74on a population with a mean FVC of84% with a nullhypothesisthatm determined the standard deviation wa(1.2 What was the power of the test at 95% confidence? ean FVC was equal to 76%,The prior research

answer choice:

A. ~99%

B. ~95%

C. ~90%

*** please explain and show me your work! im trying to understand and learn it on my own.

Answer 1

1. Assume that H₀ is true, and $\mu$ = 76

2. Find the percentile value corresponding to $\alpha$ = 0.05

sitting in the upper tail. If p(Z > z_b) = 0.05, then z_b = 1.645. Further,

1.2_ 74 Vn

3. Assume that H₀ is false, and instead $\mu$ = 84

4. Find the power by calculating the probability of getting a value more extreme than b from Step 2 in the direction of H_a. Here, you need to find p(Z > z) where

76.2295 -8455.7036 =-55.7036

Using the Z-table, you find that

Power = P(Z > -55.7036) = 1 - P(Z <= -55.7036) $\approx$ 0.99

So Option A is correct.

**If these answers do not match or any kind of confusion you have please comment