Question

Taylor Swift wanted to know if Nashville music writers had a similar income as the music writers in Austin Texas. So Taylor got the incomes of 15 randomly selected Nashville music writers and found it to be an average of 36,454 thousand dollars with a standard deviation of 12,667 dollars. She then got the income of 15 randomly selected Austin Texas music writers who had an average of 41,132 thousand dollars with a standard deviation of 19,627 dollars . What statistical test should be used to determine whether the income of music writers from these two cities differ?

Answer 1

The statistical test should be used here is "two-tailed t-test for difference of means".

Explanation: As the population standard deviations are not known here, we have to use sample standard deviation for this test, hence we will conduct a "t-test for difference in means" instead of "z-test for difference in means". This test is non-directional, we are only interested whether income of music writers from these two cities differ or not. Hence this is a "two-tailed t-test for difference of means".

With the null hypothesis, H0: μ1 = μ2 and the alternative hypothesis, Ha: μ1 ≠ μ2