Question

Question 27 options:

A researcher selects a sample of n = 25 from a normal population with µ = 80 and σ = 20. If the treatment is expected to increase scores by 6 points, what is the power of a two-tailed hypothesis test using α = .05?

Enter the result for each step below:

Step 1: Enter the standard error, σ_M (enter a number with 5 decimal places using only the keys "0-9" and "."):

Step 2: Enter the z-score that marks the boundary of the positive critical region under the null hypothesis (hint, if you drew out the distribution, the boundary marks the beginning of the shaded area on the right side) (enter a positive number with 5 decimal places using only the keys "0-9" and "."):

Step 3: What is the smallest sample mean that would fall within the positive critical region defined by the boundary you entered in the last blank (enter a number with 5 decimal places using only the keys "0-9" and ".")?

Step 4: Enter the z-score that would correspond to the sample mean you entered in the previous blank under the alternative hypothesis (enter a number with 5 decimalplaces using only the keys "0-9" and "."):

Final Answer: Enter the statistical power implied by the z-score from the previous blank as a proportion (e.g., 0.5111 not 51.11%) (enter a number with 5 decimalplaces using only the keys "0-9" and "."):

Answer 1

Let the normal population be N(80,20^2)

Let be the sample mean of 25 observations.

The treatment is supposed to increase the scores by 6 points. Hence

H1 : =86

Probability of type 1 error is =0.05.

(All probabilities have ben obtained from normal tables)