To evaluate the effect of a treatment, a sample of n=6 is obtained from a population with a mean of µ=80, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M=72. a. If the sample variance is s²=54, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α=.05? b. If the sample variance is s²=150, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α=.05? c. Comparing your answers for parts a and b, how does the variability of the scores in the sample influence the outcome of the hypothesis test?
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.
To evaluate the effect of a treatment, a sample of n=6 is obtained from a population with a
a. If the sample variance is s²=54, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α=.05?
b. If the sample variance is s²=150, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α=.05?
c. Comparing your answers for parts a and b, how does the variability of the scores in the sample influence the outcome of the hypothesis test?
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