The null hypothesis is true when the population means are equal.

The null hypothesis is true when the population means are equal.
true
true
false
false
A test is robust to violations of its assumptions if:

A test is robust to violations of its assumptions if the test is only slightly affected by these violations.
false
Violating the assumptions makes no difference to the validity of the test.
Even for robust tests, assumption violations will have an effect although they will be small.
true
The test results are generally accurate even if the test's assumptions are violated.
false
The assumptions are always true.
false
The test makes no assumptions.
When the null hypothesis is true, the assumptions are met, and the 0.05 level is used, the Type I error rate will be.

0.05
true
0.05
false
approximately 0.05 but not exactly 0.05
When the null hypothesis is true, the sample sizes are both 5, both distributions are normal, the sd for the one distribution is 1, the sd for the other distribution is 2, and the 0.05 level is used, the Type I error rate is.

.060
0.005
Use the simulation with these parameters. Make sure to simulate at least 100,000 experiments by setting the number of simulations to 10,000 and simulating at least 10 times.
The test is slightly conservative with the actual type I error rate being 0.06 rather than the nominal rate of 0.05.
When the null hypothesis is true, the sample sizes are both 20, both distributions are normal, the sd for the one distribution is 1, the sd for the other distribution is 2, and the 0.05 level is used, the Type I error rate is.

.052
0.005
Use the simulation with these parameters. Make sure to simulate at least 100,000 experiments by setting the number of simulations to 10,000 and simulating at least 10 times.
The test is very slightly conservative with the actual type I error rate being 0.052 rather than the nominal rate of 0.050.
When the null hypothesis is true, both distributions are normal, the sd for the one distribution is 1, the sd for the other distribution is 2, the sample size for the distribution with an sd of 1 is 20, the sample size for the distribution with an sd of 2 is 5, and the 0.05 level is used, the Type I error rate is.

.184
0.005
Use the simulation with these parameters. Make sure to simulate at least 100,000 experiments by setting the number of simulations to 10,000 and simulating at least 10 times.
The Type I error rate is 0.184. Therefore, the t test can have a very high Type I error rate if there is heterogeneity of variance and unequal sample sizes. This occurs when the sample size from the population with the small sd is larger than the sample size from the population with the large sd.
What is the effect of violating the assumption of normality (by having skewed distributions) on the Type I error rate?

true
It typically it will be slightly lower.
false
It increases the Type I error rate.
Use the simulation with a variety of distribution shapes and sample sizes.
There are some instances in which the Type I error rate will be slightly higher than the nominal rate (.06 rather than .05 for example) but typicall it will be slightly lower.