ETS has stated that the population mean performance on the Verbal SAT was 500 with a standard deviation of 100. Texas randomly selected a sample of SAT scores from 225 high school seniors which produced a mean of 575. Texas has always boasted that their students are some of the best in the nation. Can this claim be supported by the Verbal SAT scores? Variable(s) of interest:
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.
Variable:
A variable is an attribute or the characteristic that can be measured. The value of the variable may differ for each and every unit. That is, a variable is defined as the characteristic which is recorded for each case.
Here, the performance on the verbal SAT score is measured. Hence, the variable is verbal SAT score.
Levels of measurement:
Nominal: It categorizes the objects without any natural ordering.
Ordinal: It categorizes the objects with natural ordering.
Interval: It has ordered values with the additional property of equal distances or intervals.
Ratio: It has ordered values; equal distances between values and has an absolute zero.
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