The pathogen Phytophthora capsici causes bell peppers to wilt and die. Because bell peppers are an important commercial crop, this disease has undergone a great deal of agricultural research. It is thought that too much water aids the spread of the pathogen. Two fields are under study. The first step in the research project is to compare the mean soil water content for the two fields. Units are percent water by volume of soil. Field A samples, x1: 10.2 10.7 15.3 10.6 9.9 10.0 16.6 15.1 15.2 13.8 14.1 11.4 11.5 11.0 Field B samples, x2: 8.1 8.7 8.4 7.1 8.0 7.1 13.9 12.2 13.4 11.3 12.6 12.6 12.7 12.4 11.3 12.5 (i) Use a calculator to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 = (ii) Assuming the distribution of soil water content in each field is mound-shaped and symmetric, use a 5% level of significance to test the claim that field A has, on average, a higher soil water content than field B. (a) What is the level of significance? What is the value of the sample test statistic? (Test the difference μ1 − μ2. Do not use rounded values. Round your final answer to 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.
The pathogen Phytophthora capsici causes bell peppers to wilt and die. Because bell peppers are an important commercial crop, this disease has undergone a great deal of agricultural research. It is thought that too much water aids the spread of the pathogen. Two fields are under study. The first step in the research project is to compare the
| 10.2 | 10.7 | 15.3 | 10.6 | 9.9 | 10.0 | 16.6 |
| 15.1 | 15.2 | 13.8 | 14.1 | 11.4 | 11.5 | 11.0 |
| 8.1 | 8.7 | 8.4 | 7.1 | 8.0 | 7.1 | 13.9 | 12.2 |
| 13.4 | 11.3 | 12.6 | 12.6 | 12.7 | 12.4 | 11.3 | 12.5 |
| x1 | = |
| s1 | = |
| x2 | = |
| s2 | = |
(ii) Assuming the distribution of soil water content in each field is mound-shaped and symmetric, use a 5% level of significance to test the claim that field A has, on average, a higher soil water content than field B.
(a) What is the level of significance? What is the value of the sample test statistic? (Test the difference μ1 − μ2. Do not use rounded values. Round your final answer to three decimal places.)
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