Question

1. When we conduct hypothesis testing with proportions, we have a sample size, n, and a number of successes, x. We compare our sample information to a previously collected population proportion and perform a hypothesis test to determine whether to retain or reject the null hypothesis. Suppose we collect n = 100 data points and find that of the 100 people sampled, x = 15 are left-handed. We are then asked to perform a hypothesis test to determine whether there is sufficient evidence to suggest that the proportion of left-handed people has increased from the previously measured value of 11% of the total population. WHY can't we simply say that 15/100 = 0.15 = 15% which is higher than 11% and end it right there? Why is conducting a hypothesis test necessary to answer this question? What does a hypothesis test do that a simple comparison of the two numbers doesn't do?

2. We use very specific vocabulary when we conduct hypothesis tests. We speak of "failing to reject the null" or "retaining the null". Why is this so? Do hypothesis tests PROVE the null or do they simply FAIL to disprove the null? Explain.

Answer 1

Why is conducting a hypothesis test necessary to answer this question? What does a hypothesis test do that a simple comparison of the two numbers doesn't do?

We can see that 15 is different from 11. But in hypothesis testing, we are trying to figure out if there is a significant difference between the two proportions. By significant difference, we are trying to figure out if this difference is just a chance or they come from two different distributions or populations.

2. We use very specific vocabulary when we conduct hypothesis tests. We speak of "failing to reject the null" or "retaining the null". Why is this so? Do hypothesis tests PROVE the null or do they simply FAIL to disprove the null? Explain.

The null hypothesis is the hypothesis of no difference always, its to say a neutral ground. When we test the hypothesis we are actually testing the null hypothesis and figuring out if we find a significant proof to reject the null hypothesis. If we get significant proof, we reject the null hypothesis or we don't if we don't get enough proof.

We are not proving the null hypothesis to be true or not. They are assumed to be true, but after testing, if we get enough evidence we reject it.