A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of

The power of the test is 0.67.

Step-by-step explanation:

The complete question is:

A researcher is evaluating the influence of a treatment using a sample selected from a normally  distributed population with a mean of μ = 80 and a standard deviation σ = 20. The researcher  expects a 12-point treatment effect and plans to use a two-tailed hypothesis test with α = 0.05. Compute the power of the test if the researcher uses a sample of n = 16 individuals .

Solution:

The information provided are:

The expected mean is:

The critical z-score at α = 0.05 for a two-tailed test is:

z = 1.96

*Use a z-table.

Compute the test statistic value as follows:

The power of statistical test is well-defined as the probability that we reject a false null hypothesis.

Power = Area to the right of the critical z under the assumption that H₀ is false.

Location of  critical z (in H₀ is false distribution) =

This is negative because the critical z score is to the left of the mean  of the H₀ in false distribution.

Area above z = -0 .44.

Compute the value of P (Z > -0.44) as follows:

Thus, the power of the test is 0.67.

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

step-by-step explanation:

the shape,the size and the distance