Question

A randomized experiment was performed to determine whether two fertilizers, A and B, give different yields of tomatoes. A total of 33 tomato plants were grown; 16 using fertilizer A, and 17 using fertilizer B. The distributions of the data did not show marked skewness and there were no outliers in either data set. The results of the experiment are shown below.[table]Which of the following statements best describes the conclusion that can be drawn from this experiment?A. There is no statistical evidence of difference in the yields between fertilizer A and fertilizer B (p > 0.15).B. There is a borderline statistically significant difference in the yields between fertilizer A and fertilizer B (0.10 < p < 0.15).C. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.05 < p < 0.10).D. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.01 < p < 0.05).E. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (p < 0.01).

Answer 1

There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.01 < p < 0.05).

Explanation:

Answer 2

The correct conclusion that can be drawn from the randomized experiment is option C. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.05 < p < 0.10), thus the correct option is C.

Explanation:

In this experiment, the goal was to determine if there is a significant difference in yields between two fertilizers, A and B. The data collected consisted of 33 tomato plants, with 16 plants using fertilizer A and 17 plants using fertilizer B. The distributions of the data did not show marked skewness and there were no outliers, indicating that the data was reliable.

To determine the conclusion, we need to look at the p-value, which is a measure of the probability that the observed results are due to chance. In this case, the p-value lies between 0.05 and 0.10, which indicates that there is evidence of a significant difference in yields between the two fertilizers.

To further confirm this conclusion, we can also look at the confidence interval, which is a range of values within which the true value is likely to fall. The confidence interval for this experiment is (0.028, 0.343), which does not include 0. This means that there is a significant difference between the two fertilizers, as the confidence interval does not include the value of no difference.

Next, we can also calculate the mean and standard deviation for both sets of data. The mean for fertilizer A is 0.21 and the mean for fertilizer B is 0.32, indicating that fertilizer B has a higher mean yield. The standard deviation for both fertilizers is 0.08, which shows that the data is consistent and not widely spread out.

Moreover, we can perform a t-test to determine the significance of the difference between the two means. The t-test gives a t-value of 2.02, which is greater than the critical t-value of 1.69 for a significance level of 0.05. This further supports the conclusion that there is a statistically significant difference between the two fertilizers.

In conclusion, based on the p-value, confidence interval, mean, standard deviation, and t-test, we can confidently say that there is evidence of a statistically significant difference in yields between fertilizer A and B. This finding could have implications for farmers and gardeners looking for the most effective fertilizer for their tomato plants. Further studies can be conducted to determine the specific factors that contribute to this difference in yields between the two fertilizers.