# Significance Tests / Hypothesis Testing

The probability that was calculated above, 0.030, is the probability of getting 17 or fewer males out of 48. It would be significant, using the conventional PP=0.03 value found by adding the probabilities of getting 17 or fewer males. This is called a one-tailed probability, because you are adding the probabilities in only one tail of the distribution shown in the figure. However, if your null hypothesis is "The proportion of males is 0.5", then your alternative hypothesis is "The proportion of males is different from 0.5." In that case, you should add the probability of getting 17 or fewer females to the probability of getting 17 or fewer males. This is called a two-tailed probability. If you do that with the chicken result, you get P=0.06, which is not quite significant.

## Hypothesis testing is the subject of this chapter.

### Customarily, the alternative hypothesis is

The critical value(s) of the test statistic you would use is (are): (a) -1.96, 1.96 (d) -1.645 (b) 1.96 (e) -2.060, 2.060 (c) 1.645 (f) 1.7082140-1

### For example, the alternative hypothesis is

This proce- dure can be viewed as a test of the hypothesis p = .05 against the alternative p > .05, p being the probability that the machine turns out a defective item.

## State any assumptions you made in testing the given hypothesis.

At first glance it makes sense, but the consequence of making a false alarm could be costly. For example, silicone breast implants have been commonly available since 1963, and Dow Corning was the major chemical company that manufactures silicone gel. But after some women who received the implant complained that they were very ill and the possible cause was the silicone gel, the US Food and Drug Administration (FDA) conducted a review and decided there wasn't enough data to show silicone breast implants were safe. As a precautionary measure, the FDA banned all silicone breast implants from 1992-2006. It is important to point out that the FDA did not have evidence to indicate that silicone breast implants are unsafe; rather, it demanded the evidence to ensure its safety. But the FDA's ban had triggered a massive flood of lawsuits against Dow Corning. In 1993 Dow Corning lost more than \$287 million. Consequently, Dow Corning was under Chapter 11 protection from 1993-2004. Nonetheless, later many independent scientific studies, including the one conducted by U.S. Institute of Medicine (IOM), found that silicone breast implants do not seem to cause breast cancers or any fatal diseases. But the company's reputation had severely damaged, almost beyond redemption (Gardner, 2008).

### Suppose we arbitrarily choose to accept the null hypothesis if

Typically in a hypothesis test, the claim being made is about a population (one number that characterizes the entire population). Because parameters tend to be unknown quantities, everyone wants to make claims about what their values may be. For example, the claim that 25% (or 0.25) of all women have varicose veins is a claim about the proportion (that’s the ) of all women (that’s the ) who have varicose veins (that’s the — having or not having varicose veins).

### After that, we study hypothesis testing

Mickey -UCLA Multiple ChoiceTESTING CONCEPT STATISTICST= 2 ComputationD= 3 GeneralBack to 1299-2Back to 1301-1Back to 1301-2

### Choose an appropriate TS and compute the observed test statistic.

If the absolute value of the t-value is greater than the critical value, you reject the null hypothesis. If the absolute value of the t-value is less than the critical value, you fail to reject the null hypothesis. You can calculate the critical value in Minitab or find the critical value from a t-distribution table in most statistics books. For more information calculating the critical value in Minitab, go to and click Use the ICDF to calculate critical values.