Height of children and the nondirectional hypothesis.

Question

Betty, an employee of Shining Sun Daycare Center, read an article in Healthy Child Magazine saying that the average 3 year old child is 37 inches tall. Betty works with 3 year olds at Shining Sun, so later that week, she measured the height of each child who had just turned or was about to turn 3 years old. Here are their heights in inches, 41,40,36,42,39,38,33,44,39,41. a. State the nondirectional hypothesis

Answer 1

The non-directional hypothesis is the alternative hypothesis with "two tails". In this case it's simply the statement (or claim) that the mean height of the children is not 37 inches. It could be less than or more than. The statement that the height is expected to be 37 inches is called the null hypothesis, which is the status quo or generally accepted prevalent belief. A one-tailed alternative hypothesis would imply a statement that the height is greater than 37 inches; or a statement that the height is less than 37 inches. The non-directional hypothesis doesn't care whether it's less than or greater; just different from. This difference between a non-directional hypothesis and a directional hypothesis (specifically less than or specifically greater than) is an important difference in statistics because it affects the probability when applying a significance or confidence level about the truth of a statement. In other words: is there enough evidence to reject the null hypothesis? If there is (within an agreed confidence level), then the null hypothesis should be rejected, strongly suggesting that the alternative hypothesis should be accepted.