Select the two options that are True statements about two sample t-tests.
1. The critical values for the two-sample t-test with unequal variances and the two sample z-test, for given sample sizes, are always the same.
2. A researcher has collected two samples of data and the sample standard deviations are 2.16 and 4.82 . It would not be appropriate to use the two sample t-test with a common variance.
3. A researcher has collected two samples of data and the sample variances are 0.34 and 2.11 . It would be appropriate to use the two sample t-test with a common variance.
4. The two sample t-test with unequal variances has, as its null hypothesis, that the variances of the two populations involved are the same.
5. The same formula is used for the ESE ( estimated standard error ) in the two sample t-test with unequal variances and the two sample z-test.
(1) False. In general the critical values for the two sample z-test and the two sample z-test will be different. The t-test relies on degrees of freedom -- for very large samples the critical values will be the same.
(2) True. You can do a two sample t-test either assuming the variances are equal or not equal. Here the standard deviations are different, so the variances will be different. Thus it would not be appropriate to use the t-test with common variance.
(3) False. The variances are not equal so you should not use the common variance procedure. (This method uses a pooled estimate of the variance.)
(4) False. If the variances are not equal, you do not assume the variances are equal.
The null-hypothesis is `H_0:mu_1=mu_2 ` . The two sample t-test compares means; you would use the `F ` -test to compare variances.
(5) False. The two sample z-test uses `sigma ^2` , the population variance while the two sample t-test uses `s^2 ` , the sample variances.