Rejection Region for Two-Tailed Z Test (H1: μ ≠ μ 0 ) with α =0.05

Rejection region: the set of values for the test statistic that leads to rejection of Ho.

Now consider tests with intermediate critical regions bounded by .


A hypothesis is an educated guess about something in the world around you. It should be testable, either by experiment or observation. For example:

Very Informative.I have one doubt, why we always interested in Rejecting null hypothesis?

How does a negative z-score effect the critical region of the test?

You will still reject the null hypothesis of no difference, if the class sample is either much higher or much lower than our population mean of 75.

It is the probability of rejecting the null hypothesis when it is true.


Solution First, we write write down the null and alternative hypothesesThis is a lefttailed test. The -score that corresponds to is . The critical region is the areathat lies to the left of . If thez-value is less than there we will reject thenull hypothesis and accept the alternative hypothesis. If it is greaterthan , we will fail to reject the nullhypothesis and say that the test was not statistically significant.Wehave There is another way to interpret the test statistic.

Many authors talk about rejecting the null hypothesis in favor of the alternative.


what are examples of the alternate hypothesis and rejection region

If Step 6 is greater than Step 5, reject the null hypothesis. If it’s less than Step 5, you cannot reject the null hypothesis. In this case, it is greater (4.56 > 1.645), so you can reject the null.

What is a Rejection Region? - YouTube

If the test statistic falls in the rejection region--that is, if the statistic is a value that is in the rejection region--the null hypothesis is rejected.

Rejection region in hypothesis testing using Students t …

The isn’t used very often (because we rarely know the actual population ). However, it’s a good idea to understand how it works as it’s one of the simplest tests you can perform in hypothesis testing. In English class you got to learn the basics (like grammar and spelling) before you could write a story; think of one sample z tests as the foundation for understanding more complex hypothesis testing. This page contains two hypothesis testing examples for .

Rejection region in hypothesis testing using Students t-test

A type I error (rejecting the null hypothesis when it is true) is "convicting the innocent." A type II error (failing to reject the null hypothesis when it is false) is "letting the guilty go free." A common mistake is to confuse a type I or II error with its probability.

then you reject the null and can support the alternate hypothesis

Ten or so years ago, we believed that there were 9 planets in the solar system. Pluto was demoted as a planet in 2006. The null hypothesis of “Pluto is a planet” was replaced by “Pluto is not a planet.” Of course, rejecting the null hypothesis isn’t always that easy — the hard part is usually figuring out what your null hypothesis is in the first place.

How is the rejection region defined - Experts Mind

For example, if H0: x = y (which can be rewritten H0: x - y = 0), the test statistic is If , reject H0: x = y at the 0.05 level of significance. When we were constructing confidence intervals, it mattered whether the data were drawn from normally distributed populations, whether the population standard deviations were equal, and whether the sample sizes were large or small, The answers to these questions helped us determine the proper multiplier for the standard error.