I thought we would fail to reject the null if our p value.

So, you might get a p-value such as 0.03 (i.e., p = .03). This means that there is a 3% chance of finding a difference as large as (or larger than) the one in your study given that the null hypothesis is true. However, you want to know whether this is "statistically significant". Typically, if there was a 5% or less chance (5 times in 100 or less) that the difference in the mean exam performance between the two teaching methods (or whatever statistic you are using) is as different as observed given the null hypothesis is true, you would reject the null hypothesis and accept the alternative hypothesis. Alternately, if the chance was greater than 5% (5 times in 100 or more), you would fail to reject the null hypothesis and would not accept the alternative hypothesis. As such, in this example where p = .03, we would reject the null hypothesis and accept the alternative hypothesis. We reject it because at a significance level of 0.03 (i.e., less than a 5% chance), the result we obtained could happen too frequently for us to be confident that it was the two teaching methods that had an effect on exam performance.

the null hypothesis is rejected when it is true b.

The more this ratio deviates from 1, the more likely we are to reject the null hypothesis.
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the null hypothesis is not rejected when it is false c.

On the other hand, a Type II error — failingto reject H0 when it’s actually false — wouldPainX off the market when it actually would have helpedmore people than aspirin. This too is a bad thing.

failing to reject the null hypothesis when it is false.

Once the type of test is determined, the details of the test must be specified. Specifically, the null and alternative hypotheses must be clearly stated. The null hypothesis always reflects the "no change" or "no difference" situation. The alternative or research hypothesis reflects the investigator's belief. The investigator might hypothesize that a parameter (e.g., a mean, proportion, difference in means or proportions) will increase, will decrease or will be different under specific conditions (sometimes the conditions are different experimental conditions and other times the conditions are simply different groups of participants). Once the hypotheses are specified, data are collected and summarized. The appropriate test is then conducted according to the five step approach. If the test leads to rejection of the null hypothesis, an approximate p-value is computed to summarize the significance of the findings. When tests of hypothesis are conducted using statistical computing packages, exact p-values are computed. Because the statistical tables in this textbook are limited, we can only approximate p-values. If the test fails to reject the null hypothesis, then a weaker concluding statement is made for the following reason.

We will test the null hypothesis that the true variance is equal to 0.01.
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rejecting the null hypothesis when the alternative is true.

If you keep giving the universe opportunities to send you datathat contradict the null hypothesis, but you keep getting data that areconsistent with the null, then you begin to think that thenull hypothesis shouldn’t be rejected, that it’sactually true.

the null hypothesis is rejected when it is true.

The power is about 0.60, indicating that although the test is more likely than not to reject the null hypothesis for this value, the probability of a Type II error is high.

we reject the null hypothesis, ..

Do the sample data support the null or research hypothesis? The sample mean of 197.1 is numerically higher than 191. However, is this difference more than would be expected by chance? In hypothesis testing, we assume that the null hypothesis holds until proven otherwise. We therefore need to determine the likelihood of observing a sample mean of 197.1 or higher when the true population mean is 191 (i.e., if the null hypothesis is true or under the null hypothesis). We can compute this probability using the Central Limit Theorem. Specifically,