Hypothesis Testing: Using Equations for μ<μ0

In summary: The formula for the one-sample t-test is similar to the one-proportion z-test, but uses the sample standard deviation instead of the population standard deviation. In summary, when it comes to hypothesis testing, the first claim (H0) is always written as μ = μ0, while the second claim (H1) can be written as either μ > μ0 or μ < μ0 depending on the situation. This means that the second claim is either greater than or less than the first claim. When using tables and formulas for hypothesis testing, the hypothesis is typically listed on the left side and the critical region is listed on the right side. However, some tables may only have H1 listed as μ > μ0, so you would
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I have a question about the equations used for hypothesis testing. They all look like this one here:

H0: μ = μ0
H1: μ > μ0

For various situations.. sigma know, sigma unknown etc. So H0 is the first claim and H1 is the second claim. But this means the second claim is > than the first claim. I know you have to use something else when it's the other way around. I'm talking about the tables with the formulas. You usually have the hypothesis on the left side, and on the right side it's the critical region. But the tables I have only have H1 down as μ>μ0. But what do I do when it is < instead of > ? I attached a file that shows what I mean.
Wikipedia has a bunch of formulas. Let's take p. H1: p1>p0
Would I take the One-proportion z-test they have here ( roughly in the center of the table) ?

http://en.wikipedia.org/wiki/Statistical_hypothesis_testing

I don't know what to do if it's H1 down as μ<μ0 I hope it's somewhat clear what I'm asking for and somebody knows the answer.
 

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Yes, you would use the one-proportion z-test for a hypothesis such as H1: p1>p0. However, if your hypothesis is H1: μ<μ0, then you would use a different test, such as the one-sample t-test. The one-sample t-test is used when the population standard deviation is unknown or not given.
 

What is a hypothesis test?

A hypothesis test is a statistical method used to determine whether there is enough evidence to reject or accept a null hypothesis (μ<μ0) about a population parameter, such as a mean or proportion.

How do you perform a hypothesis test using equations?

To perform a hypothesis test using equations, you first need to state your null hypothesis and alternative hypothesis. Then, you calculate a test statistic using data from a sample and compare it to a critical value or p-value. If the test statistic falls within the critical region or has a p-value less than the significance level, you can reject the null hypothesis.

What is the significance level in a hypothesis test?

The significance level in a hypothesis test is the probability of rejecting the null hypothesis when it is actually true. This is typically set at 0.05 or 0.01, meaning that there is a 5% or 1% chance of rejecting the null hypothesis incorrectly.

What is a p-value in a hypothesis test?

A p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true. It is used to determine the significance of the results and is compared to the significance level. If the p-value is less than or equal to the significance level, the results are considered statistically significant.

What are some assumptions made in hypothesis testing using equations?

Some assumptions made in hypothesis testing using equations include a random and representative sample, normality of the population distribution, and independence of observations. Additionally, the sample size should be large enough for the central limit theorem to apply. Violating these assumptions may affect the accuracy of the results.

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