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The Amanda's house is 6.7 km far from her school.
<u>Step-by-step explanation:</u>
From the given information,
- The Amanda's school is due west of her house forms the base.
- The school is due south of the Shereen's house forms the height.
- The straight-line distance between Amanda's house and Shereen's house forms the hypotenuse.
Therefore, It can be determined that it forms the right angle triangle.
It is given that,
The distance between the school and Shereen's house is 2 kilometers.
That is, the height of the triangle = 2 km
The straight-line distance between Amanda's house and Shereen's house is 7 kilometers.
That is, the hypotenuse of the triangle = 7 km
Now, the distance between the Amanda's house and her school is the base of the triangle.
<u>To find the base :</u>
Base =
⇒
⇒
⇒
⇒ 6.7 km
Therefore, the Amanda's house is 6.7 km far from her school.
Answer:
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 <em>z</em>-score at <em>α</em> = 0.05 for a two-tailed test is:
<em>z</em> = 1.96
*Use a <em>z-</em>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 <em>z</em> under the assumption that H₀ is false.
Location of critical <em>z</em> (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.