# 11.2.2.1 - Example: Summarized Data, Equal Proportions

11.2.2.1 - Example: Summarized Data, Equal Proportions## Example: Tulips

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?

Use Minitab to conduct a hypothesis test to address this research question.

We'll go through each of the steps in the hypotheses test:

\(H_0\colon p_{white}=p_{pink}=p_{purple}=\dfrac{1}{3}\)

\(H_a\colon\) at least one \(p_i\) is not \(\dfrac{1}{3}\)

We can use the null hypothesis to check the assumption that all expected counts are at least 5.

\(Expected\;count=n (p_i)\)

All \(p_i\) are \(\frac{1}{3}\). \(30(\frac{1}{3})=10\), thus this assumption is met and we can approximate the sampling distribution using the chi-square distribution.

Let's use Minitab to calculate this.

First, enter the summarized data into a Minitab Worksheet.

C1 | C2 | |
---|---|---|

Color | Count | |

1 | White | 16 |

2 | Pink | 8 |

3 | Purple | 6 |

- After entering the data, select
*Stat > Tables > Chi-Square Goodness of Fit Test (One Variable)* - Double-click
*Count*to enter it into the*Observed Counts*box - Double-click
*Color*to enter it into the*Category names (optional)*box - Click
*OK*

This should result in the following output:

#### Chi-Square Goodness-of-Fit Test: Count

##### Observed and Expected Counts

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

White | 16 | 0.333333 | 10 | 3.6 |

Pink | 8 | 0.333333 | 10 | 0.4 |

Purple | 6 | 0.333333 | 10 | 1.6 |

##### Chi-Square Test

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

30 | 2 | 5.6 | 0.061 |

The test statistic is a Chi-Square of 5.6.

\(p>0.05\) therefore we fail to reject the null hypothesis.

There is not evidence that your tulip bulbs were not randomly selected from a population with equal proportions of white, pink and purple.