In: Math
1. Explain in words what a confidence interval means to someone who has never taken statistics.
2. There is concern that rural Minnesota is aging at a different rate than urban Minnesota. We want to test if the average age in rural Minnesota is different from the average age in urban Minnesota. Write out the null and alternative hypotheses.
3. At the 5% significance level, do you reject the null hypothesis? Why? Explain this to someone who has never taken statistics.
Hope you like the solution.
1. When we have a scientific study, or inquiry, we generally have a parameter value, that we want to check. For example, I want to take an educated guess at the number of days it might snow in the next week. We would often sought to answers like 2-4 days, i.e. it can be 2, 3 or 4 days. Here we are giving an interval in which the original value should fall. When we use statistical guesses, we can narrow down that interval with specific efficiency, i.e. suppose you have all the students' heights in your class; then you can given a 95% confidence interval say (5 feet 8 to 6 feet 3) so that the actual average is within it with 95% chance. That is if you take a 100 people, 95 out of them would have height within that range.
2. Let M1 be the average age in urban Minnesota, and M2 be the average age in rural Minnesota. Then my null hypothesis would be H0: M1 - M2 = 0, against alternate hypothesis, H1: M1 M2.
3. Well to actually reject the null hypothesis at 5% significance level, we would need a data to calculate the test with, and then decide with respect to the obtained result. In general, we reject the null hypothesis at 5% significance level, if the chance of the null hypothesis being true given what we observed is less than or equal to 5%. We generally check it with the p-value.