A popular, nationwide standardized test taken by high-school juniors and seniors may or may not measure academic potential, but we can nonetheless examine the relationship between scores on this test and performance in college. We have chosen a random sample of fifteen students just finishing their first year of college, and for each student we've recorded her score on this standardized test (from 400 to 1600) and her grade point average (from 0 to 4) for her first year in college. The data are shown below, with x denoting the score on the standardized test and y denoting the first-year college grade point average. A scatter plot of the data is shown in Figure 1. Also given is the product of the standardized test score and the grade point average for each of the fifteen students. (These products, written in the column labelled " xy", may aid in calculations.) Question table Standardized test score, x Grade point average, y xy 1090 2.25 2452.5 860 2.27 1952.2 1020 2.98 3039.6 1190 2.75 3272.5 990 2.48 2455.2 1500 3.22 4830 1400 2.95 4130 1050 2.67 2803.5 900 2.83 2547 1480 3.53 5224.4 780 2.32 1809.6 960 2.17 2083.2 1250 3.39 4237.5 1350 3.62 4887 1300 3.16 4108 What is the sample correlation coefficient for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least three decimal places.
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.
A popular, nationwide standardized test taken by high-school juniors and seniors may or may not measure academic potential, but we can nonetheless examine the relationship between scores on this test and performance in college.
We have chosen a random sample of fifteen students just finishing their first year of college, and for each student we've recorded her score on this standardized test (from
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What is the sample
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