﻿ The six most common forms of hypotheses are:

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## Usually the hypothesis concerns the value of a population parameter.

A statistical hypothesis is an examination of a portion of a population.

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# The Language of Hypothesis Testing

In the output above, Minitab reports that the P-value is 0.158. Since the P-value, 0.158, is greater than α = 0.05, the quality control specialist fails to reject the null hypothesis. There is insufficient evidence, at the α = 0.05 level, to conclude that the mean thickness of all pieces of spearmint gum differs from 7.5 one-hundredths of an inch.

Most scientific journals are prejudiced against papers that demonstrate support for null hypotheses and are unlikely to publish such papers and articles. This phenomenon leads to selective publishing of papers and ensures that the portion of articles that do get published is unrepresentative of the total research in the field.

## Here are the two opposing hypotheses:

In the output above, Minitab reports that the P-value is 0.000, which we take to mean P-value is less than 0.001, it is clearly less than α = 0.05, and the biologist rejects the null hypothesis. There is sufficient evidence, at the α = 0.05 level, to conclude that the mean height of all such sunflower seedlings is less than 15.7 cm.

We do this by comparing the sample mean and the population mean hypothesized under the null hypothesis and decide if they are "significantly different".

## Hypothesis testing is vital to test patient outcomes.

If you wanted to conduct a study on the life expectancy of Savannians, you would want to examine every single resident of Savannah. This is not practical. Therefore, you would conduct your research using a statistical hypothesis, or a sample of the Savannian population.

The null hypothesis, H0 is the commonly accepted fact; it is the opposite of the . Researchers work to reject, nullify or disprove the null hypothesis. Researchers come up with an alternate hypothesis, one that they think explains a phenomenon, and then work to .

• ### Hypothesis: Chocolate may cause pimples

Specifically, we must set a criterion about wether the sample mean is different from the hypothesized population mean.

• ### A better way to write a hypotheses is to use a formalized hypotheses

Hypothesis: I think that leaves change colors in the fall because they are not being exposed to as much sunlight.

• ### Formally we do not reject the null hypothesis.

Broken down into (somewhat) English, that’s H1 (The hypothesis): μ (the average) (is greater than) 8.2

## Formally we reject the null hypothesis.

If the biologist set her significance level α at 0.05 and used the critical value approach to conduct her hypothesis test, she would reject the null hypothesis if her test statistic t* were less than -1.6939 (determined using statistical software or a t-table):

## That’s How to State the Null Hypothesis!

The experimental results don't look different than we expect according to the null hypothesis, but they are, perhaps because the effect isn't very big.

## The biologist's hypotheses are:

The output tells us that the average height of the n = 33 sunflower seedlings was 13.664 with a standard deviation of 2.544. (The standard error of the mean "SE Mean", calculated by dividing the standard deviation 13.664 by the square root of n = 33, is 0.443). The test statistic t* is -4.60, and the P-value, 0.000, is to three decimal places.

## Null Hypothesis Definition and Example

The biologist entered her data into Minitab and requested that the "one-sample t-test" be conducted for the above hypotheses. She obtained the following output:

## Null Hypothesis Glossary Definition

These examples contain the words, if and then. Formalized hypotheses contain two variables. One is "independent" and the other is "dependent." The independent variable is the one you, the scientist control and the dependent variable is the one that you observe and/or measure the results.

## The quality control specialist's hypotheses are:

Since the biologist's test statistic, t* = -4.60, is less than -1.6939, the biologist rejects the null hypothesis. That is, the test statistic falls in the "critical region." There is sufficient evidence, at the α = 0.05 level, to conclude that the mean height of all such sunflower seedlings is less than 15.7 cm.

## There are four steps involved in hypothesis testing:

Figure out the . The alternate hypothesis is the opposite of the null hypothesis. In other words, what happens if our experiment makes a difference?

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