# 11.2.2 - Minitab Express: Goodness-of-Fit Test

11.2.2 - Minitab Express: Goodness-of-Fit Test## Research Question:

When randomly selecting a card from a deck with replacement, are we equally likely to select a heart, diamond, spade, and club?

I randomly selected a card from a standard deck 40 times with replacement. I pulled 13 hearts, 8 diamonds, 8 spades, and 11 clubs.

## MinitabExpress – Conducting a Chi-Square Goodness-of-Fit Test

### Summarized Data, Equal Proportions

To perform a chi-square goodness-of-fit test in Minitab Express using summarized data we first need to enter the data into the worksheet. Below you can see that we have one column with the names of each group and one column with the observed counts for each group.

Suit | Count | |
---|---|---|

1 | Hearts | 13 |

2 | Diamonds | 8 |

3 | Spades | 8 |

4 | Clubs | 11 |

- On a
**PC**: Select**STATISTICS > Chi-Square Goodness-of-Fit**

On a**Mac**: Select**Statistics**> Tables > Chi-Square Goodness-of-Fit - From the drop-down box select
*Summarized data in a column* - Double-click
*Count*to enter it into the*Observed Counts*box - Double-click
*Suit*to enter it into the*Category names*box - Click
*OK*

This should result in the following output:

Category | Observed | Test Proportion |
Expected | Contribution to Chi-Sq |
---|---|---|---|---|

Hearts | 13 | 0.250000 | 10 | 0.90 |

Diamonds | 8 | 0.250000 | 10 | 0.40 |

Spades | 8 | 0.250000 | 10 | 0.40 |

Clubs | 11 | 0.250000 | 10 | 0.10 |

N | DF | Chi-Sq | P-Value |
---|---|---|---|

40 | 3 | 1.80 | 0.6149 |

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

All expected values are at least 5 so we can use the chi-square distribution to approximate the sampling distribution. Our results are \(\chi^2 (3) = 1.80\). \(p = 0.6149\). Because our p-value is greater than the standard alpha level of 0.05, we fail to reject the null hypothesis. There is not evidence that the proportions are different in the population.

The example above tested equal population proportions. Minitab Express also has the ability to conduct a chi-square goodness-of-fit test when the hypothesized population proportions are not all equal. To do this, you can choose to test specified proportions or to use proportions based on historical counts:

# 11.2.2.1 - Video Example: Tulips (Summarized Data, Equal Proportions)

11.2.2.1 - Video Example: Tulips (Summarized Data, Equal Proportions)A company selling tulip bulbs claims they have equal proportions of white, pink, and purple bulbs and that they fill customer orders by randomly selecting bulbs from the population of all of their bulbs.

You ordered 30 bulbs and received 16 white, 8 pink, and 6 purple.

Is there evidence the bulbs you received were not randomly selected from a population with an equal proportion of each color?

Minitab Express is used to conduct a hypothesis test to address this research question.