The table below shows percentage changes (xi) in the Dow-Jones index over the first five trading days of each of thirteen years and also the corresponding percentage changes (yi) in another index. xi yi 1.5 14.9 0.2 -9.2 -0.1 19.6 2.8 20.3 2.2 -3.7 -1.6 27.7 -1.3 22.6 5.6 2.3 -1.4 11.9 1.4 27.0 1.5 -4.3 -4.7 20.3 1.1 4.2 1- Calculate the sample correlation and interpret. 2- Test at the 1% significance level, against a two-sided alternative, the null hypothesis that the population correlation is 0.
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.
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xi |
yi |
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1.5 |
14.9 |
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0.2 |
-9.2 |
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-0.1 |
19.6 |
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2.8 |
20.3 |
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2.2 |
-3.7 |
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-1.6 |
27.7 |
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-1.3 |
22.6 |
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5.6 |
2.3 |
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-1.4 |
11.9 |
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1.4 |
27.0 |
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1.5 |
-4.3 |
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-4.7 |
20.3 |
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1.1 |
4.2 |
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1- Calculate the sample
2- Test at the 1% significance level, against a two-sided alternative, the null hypothesis that the population correlation is 0.
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