As an economics class project, Debbie studied a random sample of 14 stocks. For each of these stocks, she found the cost per share (in dollars) and ranked each of the stocks according to cost. After 3 months, she found the earnings per share for each stock (in dollars). Again, Debbie ranked each of the stocks according to earnings. The way Debbie ranked, higher ranks mean higher cost and higher earnings. The results follow, where x is the rank in cost and y is the rank in earnings. Stock 1 2 3 4 5 6 7 8 9 10 11 12 13 14 x rank 4 12 5 7 8 11 9 13 10 6 2 3 14 1 y rank 9 7 11 14 6 10 12 5 4 3 2 1 13 8 Using a 0.01 level of significance, test the claim that there is a monotone relation, either way, between the ranks of cost and earnings. (a) What is the level of significance? (b) Compute the sample test statistic. (Use 3 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.
As an economics class project, Debbie studied a random sample of 14 stocks. For each of these stocks, she found the cost per share (in dollars) and ranked each of the stocks according to cost. After 3 months, she found the earnings per share for each stock (in dollars). Again, Debbie ranked each of the stocks according to earnings. The way Debbie ranked, higher ranks mean higher cost and higher earnings. The results follow, where x is the rank in cost and y is the rank in earnings.
| Stock | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
| x rank | 4 | 12 | 5 | 7 | 8 | 11 | 9 | 13 | 10 | 6 | 2 | 3 | 14 | 1 |
| y rank | 9 | 7 | 11 | 14 | 6 | 10 | 12 | 5 | 4 | 3 | 2 | 1 | 13 | 8 |
Using a 0.01 level of significance, test the claim that there is a monotone relation, either way, between the ranks of cost and earnings.
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