(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...

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(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.

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