A researcher develops a new exercise regimen for influencing muscle strength. The researcher knows that scores on a well-validated measure of muscle strength are normally distributed with µ = 15 and σ = 4. The researcher administers their new exercise regimen to a sample of n = 64 adults who subsequently score M = 16.5 on the measure of muscle strength. Which conclusion can the researcher make based on the results of this research study? a. The new exercise regimen has an effect on muscle strength because the computed z-score reaches the z = ±1.96 threshold. b. The new exercise regimen has an effect on muscle strength because the computed z-score does not reach the z = ±1.96 threshold. c. The new exercise regimen does not have an effect on muscle strength because the computed z-score reaches the z = ±1.96 threshold. d. The new exercise regimen does not have an effect on muscle strength because the computed z-score does not reach the z = ±1.96 threshold.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
a. |
The new exercise regimen has an effect on muscle strength because the computed z-score reaches the z = ±1.96 threshold.
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b. |
The new exercise regimen has an effect on muscle strength because the computed z-score does not reach the z = ±1.96 threshold.
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c. |
The new exercise regimen does not have an effect on muscle strength because the computed z-score reaches the z = ±1.96 threshold.
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d. |
The new exercise regimen does not have an effect on muscle strength because the computed z-score does not reach the z = ±1.96 threshold.
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