A farmer is testing the effects of 4 different fertilizers on the yields of a certain variety of tomato plants. The four fertilizers are applied to each of 5 different tomato plants and the numbers of tomatoes produced by each plant are recorded. The table below shows the results: Fertilizer A Fertilizer B Fertilizer C Fertilizer D Mean 34.6 20.2 34.6 31.6 Standard deviation 3.8 4.0 4.7 2.3 An ANOVA test is to be done, using a significance level of 0.05 A. How many degrees of freedom are there for the numerator? B. How many degrees of freedom are there for the denominator? C. What is the critical value? D. Compute the value of the variance of the means, reporting it to the exact value of 2 decimal places. E. Compute the value of the mean of the variances, reporting it to the exact value of 3 decimal places. F. Compute the test statistic, rounding the answer to 3 decimal places. G. Using the rounded test statistic, compute the p-value. 4.0156 0.000041456 -4.0156 correct answer is not given H. Based on the above, are the population means considered to be all equal? yes no
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 farmer is testing the effects of 4 different fertilizers on the yields of a certain variety of tomato plants. The four fertilizers are applied to each of 5 different tomato plants and the numbers of tomatoes produced by each plant are recorded. The table below shows the results:
| Fertilizer A | Fertilizer B | Fertilizer C | Fertilizer D | |
| 34.6 | 20.2 | 34.6 | 31.6 | |
| Standard deviation | 3.8 | 4.0 | 4.7 | 2.3 |
An ANOVA test is to be done, using a significance level of 0.05
A. How many degrees of freedom are there for the numerator?
B. How many degrees of freedom are there for the denominator?
C. What is the critical value?
D. Compute the value of the variance of the means, reporting it to the exact value of 2 decimal places.
E. Compute the value of the mean of the variances, reporting it to the exact value of 3 decimal places.
F. Compute the test statistic, rounding the answer to 3 decimal places.
G. Using the rounded test statistic, compute the p-value.
- 4.0156
- 0.000041456
- -4.0156
- correct answer is not given
H. Based on the above, are the population means considered to be all equal?
- yes
- no
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