Question

researchers wondered if the average water temperature of streams without tailed frogs was different than the average water temperature of streams with tailed frogs, which is known to be 12.2 degrees celsius. a survey of 31 streams without tailed frogs was taken and the water temperature was recorded for each stream. which of the following is the correct statement of what a type i error is in the context of this problem?
choose the correct answer below.
a. researchers found evidence that the average water temperature of streams without tailed frogs was different than the average water temperature of streams with tailed frogs when there was no difference in the average temperatures.
b. researchers found no evidence that the average water temperature of streams without tailed frogs was different than the average water temperature of streams with tailed frogs and there really was no difference in the average temperatures.
c. researchers found evidence that the average water temperature of streams without tailed frogs was different than the average water temperature of streams with tailed frogs and there really was a difference in the average temperatures.
d. researchers found no evidence that the average water temperature of streams without tailed frogs was different than the average water temperature of streams with tailed frogs when there was a difference in the average temperatures.

Explanation:

A Type I Error is rejecting the null hypothesis when it is actually true. In this context, the null hypothesis would be that the average water temperature of streams without tailed frogs is the same as the average water temperature of streams with tailed frogs (which is known to be 12.2 degrees Celsius).

• Option A: Rejecting the null hypothesis (finding evidence of a difference) when the null hypothesis is true (no actual difference) is a Type I Error.
• Option B: Failing to reject the null hypothesis when it is true is a correct decision, not a Type I Error.
• Option C: Rejecting the null hypothesis when it is false (there is a difference) is a correct decision (power of the test), not a Type I Error.
• Option D: Failing to reject the null hypothesis when it is false is a Type II Error.

Answer:

A. Researchers found evidence that the average water temperature of streams without tailed frogs was different than the average water temperature of streams with tailed frogs when there was no difference in the average temperatures