Question

SITUATION HYPOTHESIS TESTING TOOL:

I work at a radio station that also has an app, where you can upgrade to a premium product. The premium app makes it possible to swipe away more songs you don’t like. The data will be relating to the age of the costumers buying premium packages. (The age is very important for our radio station, as we are targeting a very young audience).

Null Hypothesis & Alternate Hypothesis:

H₀ : μ = 20

H₁: μ ≠ 20

Type 1 error could be that we conclude that the age is greater than 20, when it is actually not.

Type 2 error could be that we conclude that the age is greater than 20, when it actually is.

Imagine the p-value is 0.01, I would conclude that there is substantial evidence against H₀ and that it can be rejected. The result is very efficient and my assumption about the audience is not true.

Imagine the p-value is 0.20, I would conclude that H₀ is ok but still not super sure. With the p-value of 0.01, the probability was only 1 % and therefore made it very unlikely but with a p-value of 0.20, there is 20% probability. The H₀ is ok to be rejected by mistake with a 20 % probability. The result is not very efficient.

Feedback:

If young audience is important, your hypothesis should be \mu>=20 \mu<20. If the test result is to reject the null, then you know you do have a young audience. Your interpretations of type 1 and II errors are not consistent with your hypotheses. And they are opposite with the above hypotheses - how can I change it?

Questions

Reformulate your hypothesis test from above incorporate a 2-sample hypothesis test. What would be your data? What is your null hypothesis? What is your alternate hypothesis? What would be your Type 1 and Type 2 errors relative to your decision? Suppose you have a p-value of 0.01, what does this mean relative to your problem and decision? Suppose the p-value is 0.20, what does this mean relative to your problem and decision?

If you reformulated your design for 3 or more samples, what would be the implications of interaction? When would you use Tukey-Kramer test?

Answer 1

Solution :

Given that