# 5.6 - Randomization Tests in Minitab Express

5.6 - Randomization Tests in Minitab ExpressIn this lesson you have learned how to construct randomization distributions and conduct randomization tests for one group's proportion or mean using StatKey. Minitab Express can also be used to conduct randomization tests which you will learn here.

Both of the examples below use the data set:

Which contains data collected from a representative sample of STAT 200 students at the beginning of the Fall 2016 semester.

## MinitabExpress – Conducting a Randomization Test for a Proportion

**Research question:** Is the percent of all STAT 200 students who own a dog different from 50%?

- Open the data set:
- On a
**PC**: Select**STATISTICS****> Resampling > Randomization Tests > 1-Sample Proportion**

On a**Mac**: Select**Statistics > Resampling > Randomization Test for 1-Sample Proportion** - Double click the variable
*Dogs*in the box on the left to insert the variable into the*Sample*box - Use the default
*Event*of*Yes*(i.e., the event of interest is owning a dog) - Use the default
*Number of resamples*, 1000 - For
*Hypothesized proportion*enter*0.50* - Click on the
*Options*tab - The default
*Alternative hypothesis*is*Proportion ≠ hypothesized value*, this is a two-tailed test - Click OK

This should result in output similar to the output below. Note that your results may be slightly different due to random sampling variation.

Select your operating system below to see a step-by-step guide for this example.

## MinitabExpress – Conducting a Randomization Test for a Mean

**Research question: **Is there evidence that the mean height in the population of all STAT 200 students is different from 66 inches?

- Open the data set:
- On a
**PC**: Select**STATISTICS****> Resampling >****Randomization Tests > 1-Sample Mean**

On a**Mac**: Select**Statistics > Resampling >****Randomization Test for 1-Sample Mean** - Double click the variable
*Height*in the box on the left to insert the variable into the*Sample*box - Use the default number of resamples, 1000
- For
*Hypothesized mean*enter*66* - Click on the
*Options*tab - The default
*Alternative hypothesis*is*Mean ≠ hypothesized value*, this is a two-tailed test - Click OK

This should result in output similar to the output below. Note that your results may be slightly different due to random sampling variation.

Select your operating system below to see a step-by-step guide for this example.

# 5.6.1 - Example: Game of Life

5.6.1 - Example: Game of LifeA family is playing The Game of Life. This is a board game with a plastic spinner in the center. The spinner has 10 slots. The player who is the police officer collects \$5,000 every time a player spins a 10. Mom has been the police officer for the majority of the game and only twice has a player spun a 10! She wants to test if the spinner is fair. If the spinner is fair then it should result in a 10 in 10% of spins (i.e., \(p=\frac{1}{10}\)). While Mom was the police officer the wheel was spun 52 times. In those 52 spins, 2 were 10s for a sample proportion of \(\widehat{p}=\frac{2}{52}=0.038\).

Let's use the information in this scenario to determine if there is evidence that the spinner is unfair (i.e., \(p \ne 0.10\)).

If the spinner is fair then \(p=0.10\). This statement include an equality so this is our null hypothesis. Our alternative hypothesis is that the spinner is not fair.

\(H_0: p=0.10\)

\(H_a: p \ne 0.10\)

# 5.6.2 - Example: Bread Sandwiches

5.6.2 - Example: Bread SandwichesData concerning sales at one student-run cafe may be retrieved from:

And more information about this data set is available at:

We want to know if there is evidence that the mean number of bread sandwiches sold is greater than 4 in the population of all days. This scenario results in the following hypotheses:

- \(H_0: \mu = 4\)
- \(H_a: \mu > 4\)

# 5.6.3 - Example: Mean Height

5.6.3 - Example: Mean HeightThis example uses data collected from World Campus STAT 200 students at the beginning of the Fall 2016 semester. You can download this Minitab Express file here:

**Research question**: Is the mean height in the population of all World Campus STAT 200 students different from 65 inches?

This research question translates to the following hypotheses:

- \(H_0: \mu = 65\)
- \(H_a: \mu \ne 65\)