Question

1. What criteria should be used for using the 2 sample Z statistic?

2.  Comparing Population Means with Unknown Population Standard Deviations - When using the 2 sample t test (pooled t test) what are the two major differences from using the 2 Sample Z test?

3.  Unequal Population Standard Deviations - if it is not reasonable to assume the population standard deviations are equal - what is the solution?

4. For Dependent samples, what test statistic would we use? What are we investigating?

Answer 1

1. There are following requirement for using 2 sample Z statistic.

a. The two sample should be independent.
b. The two samples come from normal distribution with known standard Deviations .

2. a. In two sample t test the standard deviations are unkown.
    b. Two sample Z test is used for large data set, but two sample t test may be helpfull in smaller sample size also.

3. If the population Standard Deviations are not equal then we can not use two sample t test. We should use Welch's t-test in which population Standard Deviations are unequal.

4. For dependent samples, we use paired t- test statistic. In this test, the sample observations are paired and thus the sample sizes are equal. Here, we investigate that if the sample means differ significantly or not.