Cola Weights Identify the value of the test statistic in the display included with Exercise 1. In general, do larger test statistics result in larger P-values, smaller P-values, or P-values that are unrelated to the value of the test statistic?

Refer to Exercise 1 for the results of the analysis of variance test. The analysis of variance test is conducted to test the difference in the mean weights of the four samples of cola.

The image of the Minitab result is obtained from the reference exercise as

In the analysis of variance test, the results are based on F-test statistic.The minitab result includes the value under the column F-value against the row named ‘factor’.

Thus, the value of the test statistic is 503.06.

In an analysis of variance test, the p-value is the probability that the difference in the means is due to chance and does not exist in reality. It is the probability that the values larger than the test statistic value are obtained on the distribution.

It is observed that larger values of test statistics have smaller p-values, and smaller values of test statistics have larger p-values. It is because,as the test statistic value gets extreme (larger in the case of a right-tailed test), the chances of getting values larger than them is very small.

Here, the F-statistic to test the significance of the difference in the mean weights is equal to 503.06.

This value is very large among the values that the F-distribution can hold.

Thus, the corresponding p-value is extremely small and equal to 0.000.

Therefore, the larger test statistics have smaller p-values.