Answer :
Final answer:
Based on the F-test performed, there is evidence of a relationship between the height of the California redwood tree, the diameter of the tree four feet off the ground, and the bark thickness.
Explanation:
To determine the conclusion, we need to perform an F-test using the given information. The F-test compares the variation between groups (SSR) to the total variation (SST) and calculates a test statistic. The test statistic is then compared to a critical value at a given significance level (alpha) to determine if there is evidence of a relationship between the variables.
In this case, we are comparing the relationship between the height of the California redwood tree, the diameter of the tree four feet off the ground, and the bark thickness. The F-test will help us determine if there is evidence of a relationship between these variables.
Based on the given information, SSR is 25.04 and SST is 59.1. The degrees of freedom total is 20, and the significance level (alpha) is 0.05.
To perform the F-test, we calculate the F-statistic using the formula:
F = (SSR / df1) / (SST / df2)
where df1 is the degrees of freedom for the numerator (SSR) and df2 is the degrees of freedom for the denominator (SST).
Substituting the given values, we have:
F = (25.04 / df1) / (59.1 / df2)
Since the degrees of freedom total is 20, we can calculate the degrees of freedom for the numerator and denominator as follows:
df1 = number of groups - 1 = 3 - 1 = 2
df2 = degrees of freedom total - number of groups = 20 - 3 = 17
Substituting the degrees of freedom values, we have:
F = (25.04 / 2) / (59.1 / 17)
Simplifying the expression, we get:
F = 8.35
Next, we compare the calculated F-statistic to the critical value at the given significance level (alpha). Since alpha is 0.05, we can consult the F-distribution table or use statistical software to find the critical value.
If the calculated F-statistic is greater than the critical value, we reject the null hypothesis and conclude that there is evidence of a relationship between the variables. If the calculated F-statistic is less than the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence of a relationship between the variables.
Based on the calculated F-statistic of 8.35, we compare it to the critical value at alpha = 0.05. If the critical value is less than 8.35, we reject the null hypothesis and conclude that there is evidence of a relationship between the height of the California redwood tree, the diameter of the tree four feet off the ground, and the bark thickness. If the critical value is greater than 8.35, we fail to reject the null hypothesis and conclude that there is not enough evidence of a relationship between the variables.
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