A statistics instructor at a large western university would like to examine the relationship (if any) between the number of optional homework problems students do during the semester and their final course grade. She randomly selects 12 students for study and asks them to keep track of the number of these problems completed during the course of the semester. At the end of the class each student's total is recorded along with their final grade. Problems 57 58 62 65 68 76 77 78 78 84 85 91 Grade 62 66 66 67 72 73 72 78 73 76 75 68 1. For this setting identify the response variable. For this setting, identify the predictor variable. 2. Find the following a. Compute the linear correlation coefficient r for this data set. b. Test for a significant linear correlation. c. Classify the direction and strength of the correlation. i. Direction: ii. Strength: d. Equation of the least-squares regression line. 84 e. What is the valid prediction range for this setting? f. Test the significant of the regression line. g. Use the regression equation to predict a student's final course grade if 75 optional homework assignments are done. h. Use the regression equation to predict a student's final course grade if 45 optional homework assignments are done.

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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.