One way to evaluate the effectiveness of a teaching assistant is to examine the scores achieved by his or her students on an examination at the end of the course. Obviously, the mean score is of interest. However, the variance also contains useful information— some teachers have a style that works very well with more-able students but is unsuccessful with less-able or poorly motivated students. A professor sets a standard examination at the end of each semester for all sections of a course. The variance of the scores on this test is typically very close to 300. A new teaching assistant has a class of 30 students whose test scores had a variance of 480. Regarding these students’ test scores as a random sample from a normal population, test, against a two-sided alternative, the null hypothesis that the population variance of their scores is 300.
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.
One way to evaluate the effectiveness of a teaching assistant is to examine the scores achieved by his or her students on an examination at the end of the course. Obviously, the mean score is of interest. However, the variance also contains useful information— some teachers have a style that works very well with more-able students but is unsuccessful with less-able or poorly motivated students. A professor sets a standard examination at the end of each semester for all sections of a course. The variance of the scores on this test is typically very close to 300. A new teaching assistant has a class of 30 students whose test scores had a variance of 480. Regarding these students’ test scores as a random sample from a normal population, test, against a two-sided alternative, the null hypothesis that the population variance of their scores is 300.
Step by step
Solved in 2 steps with 1 images
