# Statdisk Instructions for Hypothesis Testing Technology Exercises

This document is set up a little bit differently than other set of instructions. There are common tasks needed for each of the questions, so I'm going to explain how to do each task in its own section rather than within the context of a particular problem.

## Randomly Selecting Dates

Statdisk won't do this, use Minitab.

## Critical Values

To look up a critical value, you need to know three things.

1. The distribution being used. This is the standard normal distribution (z) for proportions or the Student's t distribution (t) for means. If you use a t distribution, you will also need to know the degrees of freedom.
2. The significance level α. The default value used if no other value is given is α = 0.05.
3. Whether it is a one tail (left tail or right tail) or a two tail test. This comes from the alternative hypothesis, H1.

### Using the t-table

1. At the top of the t-table, there is a row for one tail areas and a row for two tail areas. Pick the appropriate row based on the type of test.
2. Scan across that row and find your significance level α.
3. Use that column and go down until you find the proper degrees of freedom. If you're using the normal distribution, go all the way to the bottom row.
4. Read your critical value(s) from the table. There should always be as many critical values as tails and the signs should agree. That is, a left tail test should have a negative critical value, a right tail test should have a positive critical value, and a two tail test should have both a positive and negative critical value.

### Using Statdisk

Statdisk will automatically give you the critical value when you perform a hypothesis test.

## Critical Values, Test Statistics, P-Values, and Confidence Intervals

This is the crux of the hypothesis test.

### Choosing the Right Test

You will need to go to Analysis / Hypothesis Testing and choose the proper kind of test. Once you have the proper test chosen, the process is very similar for each of the tests.

• Mean One Sample: Use this when you're testing a claim about a single population mean μ.
• Mean Two Independent Samples: Use this when you're testing a claim about two independent means μ1 and μ2. This is when you have two different samples that you want to compare.
• Mean Matched Pairs : Use this when you're using two dependent samples. This is better described as one sample with two different measurements for each object in the sample.

• Proportion One Sample: Use this when you're testing a claim about a single population proportion p.
• Proportion Two Samples: Use this when you're testing a claim about two population proportions p1 and p2.

When you are testing a proportion, it will ask for the number of trials (n) and the number of successes (x). It is important to note that these are both whole numbers, not percents or proportions. If you have a sample size of 425 with a 37% success rate, then the number of successes would be 0.37 * 425 = 157.25, but since it has to be a whole number, you would round that to be 157 and enter that for the number of successes.

#### One Sample vs Two

A little note about one sample versus two samples. When you are working with one sample, you need a numerical value that you can test against. That is, you will have to have a claimed value for the population mean or the population proportion. Something like μ = 15 or p = 0.34.

When you choose a test about one mean or proportion, there will be a box for the "claimed mean" or "claimed proportion". This value comes from the null hypothesis; afterall, all hypothesis testing is done under the assumption that the null hypothesis is true.

When you are working with two samples, you don't need a specific value, you are comparing them to each other. You'll take a claim like μ1 = μ2, but there is no claim that they're both equal to another value like μ1 = μ2 = 15. When you actually get around to performing the hypothesis test, you'll move both variables to the same side so the right side is 0 and get μ1 - μ2 = 0. This test is sometimes called "the difference of the means." The confidence interval generated will be for the difference of the means, not for each mean, so they should be centered around 0.

#### Original Claim

The very first menu box on each of the hypothesis test screens is for you to specify the original claim. Note that this is the original claim and not the null hypothesis, Statdisk will figure out the null and alternative hypotheses from the original claim.

There are six choices, corresponding to the six inequalities. =, <=, >=, not =, >, and <.

#### Significance Level

The other option on all of the hypothesis tests is th significance level, α. This is entered as a decimal and the default value is 0.05.

#### Entering the Summary Statistics

Statdisk, unlike Minitab, does not allow you to operate with the raw data with the exception of the paired (matched) samples t test. You must find the summary statistics first. That means you'll need to go to Data / Descriptive Statistics and choose the column to evaluate.

### Interpreting the output

Once you click evaluate, the output screen will have all of the relevant information for the hypothesis test. This includes the original claim, the sample statistics, the test statistic, critical value, p-value, and confidence interval.

Note that the confidence intervals are always two tail confidence intervals, even if it is a one tail test. The confidence level is adjusted accordingly, but this is different than what we will be teaching in class.

Do not use the confidence intervals generated by Statdisk unless you have a two tail test.

After the confidence interval, Statdisk provides the decision ( reject the null hypothesis or fail to reject the null hypothesis ). In this class, we'll use the word retain instead of the phrase "fail to reject". Statdisk also provides a conclusion, but obviously the wording isn't in the context of the original problem since it has no idea what that was.

#### Generating a Plot

If you will click on Plot, you'll get a graph of a normal or t distribution with the critical values and test statistic on it. It isn't labeled properly with all of the information we want, but it's a quick way to look at the graph.