Question

1.  What assumptions must be validated to use t-distribution methods for a single sample mean (confidence interval or hypothesis test)?

2. What assumptions must be validated to use t-distribution methods for two independent sample means (confidence interval or hypothesis test)?

Answer 1

Assumptions to use t-distribution for a single sample mean

1. The parent population from which the sample is drawn is normal.

2. The sample observations are independent, i.e. the sample is random

3. The population standard deviation is unknown

4. Sample Size should be reasonably large so that distribution of results should approach a normal bell-shaped curve

Assumptions to use t-distribution for two independent sample means

1. Normality of Distribution -  Parent populations. from which the samples have been drawn are normally distributed.

2. Homogenity of Variances - The population variances are equal and unknown. i.e .     is unknown

3. Randomness and Independence - The two samples are random and independent of each other.