The following data pertain to x, the amount of fertil-izer (in pounds) that a farmer applies to his soil, and y, his yield of wheat (in bushels per acre): xy xy xy112 33 88 24 37 2792 28 44 17 23 972 38 132 36 77 3266 17 23 14 142 38112 35 57 25 37 1388 31 111 40 127 2342 8 69 29 88 31126 37 19 12 48 3772 32 103 27 61 2552 20 141 40 71 1428 17 77 26 113 26 Assuming that the data can be looked upon as a randomsample from a bivariate normal population, calculate rand test its significance at the 0.01 level of significance.Also, draw a scattergram of these paired data and judgewhether the assumption seems reasonable.
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.
The following data pertain to x, the amount of fertil-
izer (in pounds) that a farmer applies to his soil, and y, his
yield of wheat (in bushels per acre):
xy xy xy
112 33 88 24 37 27
92 28 44 17 23 9
72 38 132 36 77 32
66 17 23 14 142 38
112 35 57 25 37 13
88 31 111 40 127 23
42 8 69 29 88 31
126 37 19 12 48 37
72 32 103 27 61 25
52 20 141 40 71 14
28 17 77 26 113 26
Assuming that the data can be looked upon as a random
sample from a bivariate normal population, calculate r
and test its significance at the 0.01 level of significance.
Also, draw a scattergram of these paired data and judge
whether the assumption seems reasonable.
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