Question

Describe an experiment that would require use of one of the three different t-tests (One Sample, Correlated Samples, or Independent Groups)

Answer 1

i) One Sample t test: Suppose the president of a company wants to claim that the average annual income in his company is greater than 50000 dollars. He asks the statistician to conduct a formal test to check if his claim is correct. So the statistician collects the data on annual income for all employess and perform the one sample t test for means. So null hypothesis is that mean is 50000 vs. alternative hypothesis is that mean is larger than 50000. He calculates the test statistic based on the data and determine the p-value. If the p-value is very small, he rejects the null hypothesis and concludes that the average annual income in his company is greater than 50000 dollars.

ii) Correlated Samples:

Let's perform the hypothesis test on the husband's age and wife's age data in which the sample correlation based on n = 170 couples is r = 0.939. Test whether is there any association between husband's age and Wife's age

iii) Independent Grops:

A t-test helps you compare whether two groups have different average values

Let’s say you’re curious about whether New Yorkers and Kansans spend a different amount of money per month on movies. It’s impractical to ask every New Yorker and Kansan about their movie spending, so instead you ask a sample of each—maybe 300 New Yorkers and 300 Kansans—and the averages are $14 and $18. The t-test asks whether that difference is probably representative of a real difference between Kansans and New Yorkers generally or whether that is most likely a meaningless statistical fluke.