Question

In this case ,Why do we use the left-tailed hypothesis instead of the right-tailed hypothesis？When do we use the right-tailed hypothesis and when do we use the left-tailed hypothesis? Explain only the above two questions and do not need to answer the following questions. Thanks!!

During the period 1990-1998 there were 46 Atlantic hurricanes, of which 19 struck the United States. During the period 1999-2006 there were 70 hurricanes, of which 45 struck the United States. (a) State the hypotheses to test whether the percentage of hurricanes that strike the United States is increasing. (b) Calculate the test statistic. (c) State the critical value at α = .01. (d) What is your conclusion? (e) Can normality of p1 2 p2 be assumed?

Answer 1

In simple terms, we get to know about the test whether right, left or two tailed from the sign used in the alternative hypothesis.

If the sign used if =/, it is a two tailed test.

If the sign used is ">", it is a right tailed test.

If the sign used is "<", it is a left tailed test.

The sign in the alternative hypothesis depends on the claim of the researcher. In this case, we have to test whether the percentage of hurricanes is increasing or Ha: p1 < p2. Hence, this is a left tailed test.
If you reverse the proportions. Ha: p2 > p1, it becomes a right tailed test. There won't be any difference in the results whatsoever.