Chapter 10, Problem T10.1SPT

To determine

To select the correct option for the question, are the conditions for performing a two-sample t test satisfied.

Answer to Problem T10.1SPT

Option (e) is the correct option.

Explanation of Solution

The conditions for performing a two sample t test are: Random, Normal and Independent.

Thus, we may look in the question for this as;

Random: It is satisfied because the samples have been given to be random samples.

Normal: It can be assumed to be satisfied because the sample size of each sample is at least $30$ .

Independent: It is satisfied because the random sample have been given to be separate and thus are independent. Moreover, the sample sizes are less than $10\%$ of the population size.

Thus we can see that all the three conditions are satisfied and thus the correct option is (e) option i.e. Yes, we have two independent random samples and large sample sizes.