Assume the null hypothesis states that the mean is at least 18 . Is this a left-tailed, or two-t

Assume the null hypothesis states that the mean is at least...

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions or inferences about population parameters based on sample data. It involves comparing observed data to a model under a hypothesis, typically testing whether a parameter meets a certain condition or not.

Null and Alternative Hypotheses

In hypothesis testing, researchers define the null hypothesis (H?) and the alternative hypothesis (H? or Ha). The null hypothesis usually represents the status quo or a statement of no effect, while the alternative hypothesis represents the claim to be tested and is typically a statement of a difference or effect.

One-Tailed Test

A one-tailed test is used when the research hypothesis predicts a specific direction of the effect. This means that the region of rejection for the test statistic is on one side of the sampling distribution, corresponding to either a lower or higher extreme, but not both.

Directional Hypotheses and Tail Interpretation

When the null hypothesis claims that a parameter is at least a certain value, the alternative hypothesis inherently becomes directional (e.g., stating the parameter is less than that value). This setup indicates a left-tailed test because the area of interest for rejecting the null hypothesis is in the lower tail of the distribution.

Transcript

00:01 Hello, welcome to the video, and today we're going to be talking about hypothesis tests, and specifically how to know which type of test we should use in certain situations.

00:13 So, in this problem, we're told that our null hypothesis states that the mean is at least 18.

00:20 And translating this into notation, we can say that mu, which represents the population mean, is greater than or equal to 18.

00:32 This can also be read as at least because we're saying that the lowest value that mu can take on is 18.

00:41 Or at least that's what's being claimed since that is what our null hypothesis.

00:46 So close.

00:59 Hello, welcome to the video, and today we're going to be talking about hypothesis tests and specifically how to know which type of test we should use in certain situations.

01:12 So, the hypothesis is, and we would like to test whether or not this is true.

01:16 So we're told what our null hypothesis is, and the question asks us whether or not we would use a two -tailed test or a left -tailed test.

01:25 We have to choose between the two.

01:28 So to answer this, we can start by determining what our alternative hypothesis is from our null.

01:35 And to do this, we can basically just claim the exact opposite of what's being said here.

01:41 So that mu is actually less than 18.

01:44 In this problem, we're told that our null hypothesis states that the mean is at least 18.

01:52 And translating this into notation, we can say that mu, which represents the population mean, is greater than or equal to 18.

02:03 This can also be read as at least because we're saying that the lowest value that mu can take on is 18.

02:13 Or at least that's what's being claimed since that is what our null hypothesis.

02:18 Next we can translate our hypotheses into this picture here...

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