# Can you reject the null hypothesis when p > 0.05

Is the acceptable level of Type I error denoted as α. Say a 5 percent of tolerance is allowed for Type I error beyond which the null hypothesis is rejected. That is out of 20 samples, we're willing to accept one rejection of null hypothesis even if it is true. α can also be 1 percent if consequences of Type I error are costly.

## (P = 0.0022), we reject the null hypothesis and conclude that the ..

### -The null hypothesis has been REJECTED at the 0.05 level

Because 2.38 __>__ 1.645, we reject the null hypothesis. (The same conclusion can be drawn by comparing the 0.0087 probability of observing a sample mean as extreme as 197.1 to the level of significance of 0.05. If the observed probability is smaller than the level of significance we reject H_{0}). Because the Z score exceeds the critical value, we conclude that the mean weight for men in 2006 is more than 191 pounds, the value reported in 2002. If we observed the second sample (i.e., sample mean =192.1), we would not be able to reject the null hypothesis because the Z score is 0.43 which is not in the rejection region (i.e., the region in the tail end of the curve above 1.645). With the second sample we do not have sufficient evidence (because we set our level of significance at 5%) to conclude that weights have increased. Again, the same conclusion can be reached by comparing probabilities. The probability of observing a sample mean as extreme as 192.1 is 33.4% which is not below our 5% level of significance.

### The answer is 2.0>1.645 and we reject the null hypothesis

The decision rule is a statement that tells under what circumstances to reject the null hypothesis. The decision rule is based on specific values of the test statistic (e.g., reject H_{0} if Z __>__ 1.645). The decision rule for a specific test depends on 3 factors: the research or alternative hypothesis, the test statistic and the level of significance. Each is discussed below.

## represents the run of 100 coin flips

The decision rule is a statement that tells under what circumstances to reject the null hypothesis. The decision rule is based on specific values of the test statistic (e.g., reject H_{0} if Z __>__ 1.645). The decision rule for a specific test depends on 3 factors: the research or alternative hypothesis, the test statistic and the level of significance. Each is discussed below.

## Say you have a set of observations O and a null hypothesis H 0

If the null hypothesis is rejected, then an exact significance level is computed to describe the likelihood of observing the sample data assuming that the null hypothesis is true. The exact level of significance is called the p-value and it will be less than the chosen level of significance if we reject H_{0}.