Based on the given information, the family error rate is 0.0975
Therefore, the correct answer is d) 0.0975.
How to determine the family error rate
To determine the family error rate for two t tests conducted at a level of α=0.05, use a tree diagram to visualize the different possible outcomes.
Let's denote the two tests as Test 1 and Test 2.
At each test, there are two possible outcomes: either we reject the null hypothesis (significant result) or we fail to reject the null hypothesis (non-significant result).
Using a tree diagram, consider the four possible combinations of outcomes for the two tests:
Test 2
/ \
/ \
Reject Fail to Reject
(Significant) (Non-Significant)
/ \
/ \
Test 1 Reject Fail to Reject
(Sig.) (Non-Sig.)
From this tree diagram, calculate the probability of obtaining a significant result for at least one of the tests, assuming the null hypothesis is true.
There are three paths that lead to a significant result: (Reject, Reject), (Reject, Fail to Reject), and (Fail to Reject, Reject).
The probability of each path can be calculated as follows:
(Reject, Reject): The probability of rejecting the null hypothesis in Test 1 is α=0.05, and the probability of rejecting the null hypothesis in Test 2 is also α=0.05. Therefore, the probability of this path is
0.05 * 0.05 = 0.0025.
(Reject, Fail to Reject): The probability of rejecting the null hypothesis in Test 1 is α=0.05, and the probability of failing to reject the null hypothesis in Test 2 is 1 - α = 1 - 0.05 = 0.95. Therefore, the probability of this path is
0.05 * 0.95 = 0.0475.
(Fail to Reject, Reject): The probability of failing to reject the null hypothesis in Test 1 is 1 - α = 1 - 0.05 = 0.95, and the probability of rejecting the null hypothesis in Test 2 is α=0.05. Therefore, the probability of this path is
0.95 * 0.05 = 0.0475.
To obtain the family error rate, we sum up the probabilities of these three paths:
0.0025 + 0.0475 + 0.0475 = 0.0975
Therefore, the correct answer is d) 0.0975.