1.Suppose the formative and summative grades in a College Algebra class for 11 students are given below: Students A B C D E F G H I J K Formative Grade 63 77 90 80 93 45 55 73 80 65 50 Summative Grade 85 100 95 97 100 80 90 97 90 92 75 Define D = Formative Grade – Summative Grade. Then what would be the mean and standard deviation of D based on the sample? (assume formative and summative grades are normally distributed) A. 70.09 and 15.85 B. 91 and 8.16 C. -20.91 and 7.69 D. -20.91 and 10.23 2. What would be the standard error in problem 1? A. 4.78 B. 3.09 C. 2.46 D. 2.32 3. What would be the computed test statistic to test for higher mean summative score based on problem 1? A. -2.04 B. -4.38 C. -6.78 D. -9.02
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.
Students A B C D E F G H I J K
Formative Grade 63 77 90 80 93 45 55 73 80 65 50
Summative Grade 85 100 95 97 100 80 90 97 90 92 75
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