Compute the test value. Round the intermediate and final answers to at least three decimal places.

MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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Compute the test value. Round the intermediate and final answers to at least three decimal places. 

### Type of Medicine and Age Relationship Study

A medical researcher is conducting a study to determine whether the type of vitamin pills taken is related to the age of the person consuming them. The dataset provided includes information on the number of people of different age groups and their preferences for different types of vitamins: Liquid, Tablet, and Gummy. The level of significance for this study is set at α = 0.10.

#### Data Summary:

The table below summarizes the data collected:

| Age Group       | Liquid | Tablet | Gummy |
|-----------------|--------|--------|-------|
| **20-39**       |   5    |   16   |   7   |
| **40-59**       |   10   |   24   |   15  |
| **60-over**     |   12   |   9    |   8   |

#### Explanation:
- Columns indicate the type of vitamin: Liquid, Tablet, and Gummy.
- Rows indicate the age groups: 20-39, 40-59, and 60-over.
- The numbers in each cell represent the count of people within each age group and their preferred type of vitamin.

#### Instructions:
- Use statistical methods to determine if there is a significant relationship between the type of vitamin preferred and the age group.
- Employ the critical value method at the α = 0.10 significance level to reach your conclusion.

This study aims to provide insights into whether age influences vitamin preferences, which can guide healthcare providers in recommending vitamin types based on patient demographics.
Transcribed Image Text:### Type of Medicine and Age Relationship Study A medical researcher is conducting a study to determine whether the type of vitamin pills taken is related to the age of the person consuming them. The dataset provided includes information on the number of people of different age groups and their preferences for different types of vitamins: Liquid, Tablet, and Gummy. The level of significance for this study is set at α = 0.10. #### Data Summary: The table below summarizes the data collected: | Age Group | Liquid | Tablet | Gummy | |-----------------|--------|--------|-------| | **20-39** | 5 | 16 | 7 | | **40-59** | 10 | 24 | 15 | | **60-over** | 12 | 9 | 8 | #### Explanation: - Columns indicate the type of vitamin: Liquid, Tablet, and Gummy. - Rows indicate the age groups: 20-39, 40-59, and 60-over. - The numbers in each cell represent the count of people within each age group and their preferred type of vitamin. #### Instructions: - Use statistical methods to determine if there is a significant relationship between the type of vitamin preferred and the age group. - Employ the critical value method at the α = 0.10 significance level to reach your conclusion. This study aims to provide insights into whether age influences vitamin preferences, which can guide healthcare providers in recommending vitamin types based on patient demographics.
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