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Answer :
Final answer:
The appropriate T-test for this experiment is the independent samples T-test. The null hypothesis (H0) assumes that there is no significant difference in the growth rates of fiddle leaf fig trees using the standard fertilizer and the NEW fertilizer. The alternative hypothesis (H1) assumes that there is a significant difference in the growth rates of fiddle leaf fig trees using the standard fertilizer and the NEW fertilizer. Using α= 0.05 and performing a two-tailed test, the critical value for the T-test is approximately ±2.228. The obtained statistics (+2.590) is greater than the critical value, leading to the rejection of the null hypothesis. This means that there is a significant difference in the growth rates of fiddle leaf fig trees using the standard fertilizer and the NEW fertilizer.
Explanation:
A. For this experiment, which T test is appropriate for hypothesis testing?
In this experiment, we are comparing the growth rates of fiddle leaf fig trees using different fertilizers. Since the trees are treated as independent groups and there is no pairing or matching involved, the appropriate T-test for this experiment is the independent samples T-test.
B. Report the null (H0) hypothesis, assuming α= 0.05, 2 tails.
The null hypothesis (H0) assumes that there is no significant difference in the growth rates of fiddle leaf fig trees using the standard fertilizer and the NEW fertilizer. In this case, the null hypothesis can be stated as:
H0: The mean growth rate of fiddle leaf fig trees using the standard fertilizer is equal to the mean growth rate of fiddle leaf fig trees using the NEW fertilizer.
C. Report the alternative (H1) hypothesis, assuming α= 0.05, 2 tails.
The alternative hypothesis (H1) assumes that there is a significant difference in the growth rates of fiddle leaf fig trees using the standard fertilizer and the NEW fertilizer. In this case, the alternative hypothesis can be stated as:
H1: The mean growth rate of fiddle leaf fig trees using the standard fertilizer is not equal to the mean growth rate of fiddle leaf fig trees using the NEW fertilizer.
D. Use α= 0.05, 2 tails, find the critical value:
When using α= 0.05 and performing a two-tailed test, the critical value for the T-test can be found using a T-distribution table or a statistical software. The critical value corresponds to the significance level (α) and the degrees of freedom (df), which is calculated as the sum of the sample sizes minus 2. In this case, since we have 6 observations in each group, the degrees of freedom is 10 (6 + 6 - 2 = 10). Using the T-distribution table or software, the critical value for α= 0.05 and 10 degrees of freedom is approximately ±2.228.
E. The obtained statistics equals (+2.590), what is the decision?
To make a decision, we compare the obtained statistics (T-value) with the critical value. If the obtained statistics falls within the critical region (beyond the critical value), we reject the null hypothesis. In this case, the obtained statistics (+2.590) is greater than the critical value of ±2.228. Therefore, we reject the null hypothesis.
F. What does your decision mean?
Rejecting the null hypothesis means that there is a significant difference in the growth rates of fiddle leaf fig trees using the standard fertilizer and the NEW fertilizer. The results suggest that the NEW fertilizer has an effect on the growth rate of the trees compared to the standard fertilizer.
Learn more about t-test for hypothesis testing here:
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