An instructor has a class of 23 students. At the beginning of the semester, each student is randomly assigned to one of four teaching assistants—Smiley, Haydon, Alleline, or Bland. The students are encouraged to meet with their assigned teaching assistant to discuss difficult course material. At the end of the semester, a common examination is administered. The scores obtained by students working with these teach- ing assistants are shown in the accompanying table.Smiley Haydon Alleline Bland72 78 80 7969 93 68 7084 79 59 6176 97 75 7464 88 82 85 81 68 63a. Calculate the within-groups, between-groups, and total sum of squares.b. Complete the analysis of variance table and test the null hypothesis of equality of population mean scores for the teaching assistants.
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.
An instructor has a class of 23 students. At the beginning of the semester, each student is randomly assigned to one of four teaching assistants—Smiley, Haydon, Alleline, or Bland. The students are encouraged to meet with their assigned teaching assistant to discuss difficult course material. At the end of the semester, a common examination is administered. The scores obtained by students working with these teach- ing assistants are shown in the accompanying table.
Smiley Haydon Alleline Bland
72 78 80 79
69 93 68 70
84 79 59 61
76 97 75 74
64 88 82 85
81 68 63
a. Calculate the within-groups, between-groups, and total sum of squares.
b. Complete the analysis of variance table and test the null hypothesis of equality of population mean scores for the teaching assistants.
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