An experiment samples two independent populations X and Y. • X is sampled 26 times yielding sample mean = 34.1 and sample std dev s, = 7.2. •Y is sampled 11 times yielding sample mean j = 33.7 and sample std dev s, = 9.6. %3D Do a one-tailed, pooled variance, two-sample t-test against Ho : µx - Hy = 8. In this case, the sample mean difference is a - y = The alternative hypothesis for the one-tailed test in this case is HA : Hx - HY ?? ♥ 8. The pooled sample variance of {X;} and {Y;} is The pooled sample std. dev. of (X - Y) is The test statistic has distribution T~t( In this case, the test statistic has value t = This has p-value
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.
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