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twil85459
04.11.2020 •
Mathematics
A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of
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Ответ:
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) =![z_{\bar x}-z](/tpl/images/0866/5240/3d481.png)
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.
Ответ:
Second round: 25 people are told
Square each number.
The second round is 5 squared, so the third round will be 5 to the third, or 25 squared.
So the answer is 15,625