Sage-Tips

How do you reject a null hypothesis with a test statistic?

Compare the test statistic to the critical value. If the test statistic is more extreme in the direction of the alternative than the critical value, reject the null hypothesis in favor of the alternative hypothesis. If the test statistic is less extreme than the critical value, do not reject the null hypothesis.

What do you mean by type 1 error and Type 2 error?

In statistics, a Type I error means rejecting the null hypothesis when it’s actually true, while a Type II error means failing to reject the null hypothesis when it’s actually false.

What does it mean to reject the null hypothesis at the .05 level?

05. If there is less than a 5\% chance of a result as extreme as the sample result if the null hypothesis were true, then the null hypothesis is rejected. When this happens, the result is said to be statistically significant .

What is the probability of rejecting the null hypothesis when the null hypothesis is true known as?

Power
Power is the probability of rejecting the null hypothesis when, in fact, it is false. Power is the probability of making a correct decision (to reject the null hypothesis) when the null hypothesis is false. Power is the probability that a test of significance will pick up on an effect that is present.

When a null hypothesis Cannot be rejected we conclude that?

When we reject the null hypothesis when the null hypothesis is true. When we fail to reject the null hypothesis when the null hypothesis is false. The “reality”, or truth, about the null hypothesis is unknown and therefore we do not know if we have made the correct decision or if we committed an error.

What is alpha and beta error?

As a consequence of sampling errors, statistical significance tests sometimes yield erroneous outcomes. Specifically, two errors may occur in hypothesis tests: Alpha error occurs when the null hypothesis is erroneously rejected, and beta error occurs when the null hypothesis is wrongly retained.

What is one tailed test and two tailed test?

The Basics of a One-Tailed Test Hypothesis testing is run to determine whether a claim is true or not, given a population parameter. A test that is conducted to show whether the mean of the sample is significantly greater than and significantly less than the mean of a population is considered a two-tailed test.

What does 0.01 significance level mean?

Significance Levels. The significance level for a given hypothesis test is a value for which a P-value less than or equal to is considered statistically significant. Typical values for are 0.1, 0.05, and 0.01. These values correspond to the probability of observing such an extreme value by chance.

When null hypothesis is not rejected we conclude that?

If the null hypothesis is not rejected, we conclude that H0 is true. You just studied 16 terms!

What is the null hypothesis in statistical testing?

Thus, a statistical test requires a pair of hypotheses; namely, \\(H_0\\): a null hypothesis \\(H_a\\): an alternative hypothesis. Significance levels The null hypothesis is a statement about a belief.

When is the test statistic in the rejection region?

When the test statistic is in the rejection region, we reject the null hypothesis ( H 0 ). Here, the test statistic (TS) was ≈ 2.889 ― and the critical value was ≈ 2.462 ―

What is the rejection region for a right tailed test?

For a right tailed test we need to check if the test statistic (TS) is bigger than the critical value (CV). If the test statistic is bigger than the critical value, the test statistic is in the rejection region. When the test statistic is in the rejection region, we reject the null hypothesis ( H 0 ).

How do you test a binomial distribution with a null hypothesis?

Then, if the null hypothesis is true, that is, m = m 0, then N − and N + both follow a binomial distribution with parameters n and p = 1/2. That is: Now, suppose we are interested in testing the null hypothesis H 0: m = m 0 against the alternative hypothesis H A: m > m 0.