### Investigation of Caffeine Levels in Coffee**Introduction:**Scientists conducted an experiment to investigate the caffeine levels found in 16-ounce cups of a specific blend of coffee. For this purpose, cups of this coffee blend were purchased over six consecutive days from a specialty coffee shop. The caffeine content in each cup was measured and recorded in milligrams. The data collected is presented in the table below.**Caffeine Content Data (mg):**| Cup | Day 1 | Day 2 | Day 3 | Day 4 | Day 5 | Day 6 ||-----|-------|-------|-------|-------|-------|-------|| Caffeine (mg) | 550 | 354 | 401 | 610 | 350 | 358 |**Instructions:**- Analyze the data provided in the table.- Complete parts a through d based on the given information.**Explanation for Graphs/Diagrams:**- The table above displays the caffeine content in milligrams (mg) for each of the six cups purchased over six consecutive days.- Use statistical methods to interpret the data and draw conclusions regarding the variability and consistency of the caffeine content in the coffee blend.**Note:**This data can be utilized for various statistical analyses such as calculating the mean, median, mode, range, and standard deviation to understand the dispersion and central tendency of the caffeine content in the coffee samples. ### Hypothesis Testing for Median Caffeine Content#### a. Formulating the HypothesesSuppose the scientists are interested in determining whether the median amount of caffeine in this coffee blend exceeds 325 milligrams. Set up the null and alternative hypotheses of interest:- Null Hypothesis (H₀): η = 325- Alternative Hypothesis (Hₐ): η > 325#### b. Sample AnalysisHow many of the cups in the sample have a caffeine content that exceeds 325 milligrams?- **Answer:** 5 cups#### c. Probability CalculationAssuming that p = 0.5, find the probability that at least as many of the 6 cups as were counted in part (b) have caffeine amounts that exceed 325 milligrams.- **Answer:** The probability is 0.031 (rounded to three decimal places as needed).

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of this blend of coffee were purchased on six consecutive days from each of the six cups (measures in milligrams) is provided in the tabl 550 354 401 610 350 358

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Question

### Investigation of Caffeine Levels in Coffee

**Introduction:**
Scientists conducted an experiment to investigate the caffeine levels found in 16-ounce cups of a specific blend of coffee. For this purpose, cups of this coffee blend were purchased over six consecutive days from a specialty coffee shop. The caffeine content in each cup was measured and recorded in milligrams. The data collected is presented in the table below.

**Caffeine Content Data (mg):**

| Cup | Day 1 | Day 2 | Day 3 | Day 4 | Day 5 | Day 6 |
|-----|-------|-------|-------|-------|-------|-------|
| Caffeine (mg) | 550 | 354 | 401 | 610 | 350 | 358 |

**Instructions:**
- Analyze the data provided in the table.
- Complete parts a through d based on the given information.

**Explanation for Graphs/Diagrams:**
- The table above displays the caffeine content in milligrams (mg) for each of the six cups purchased over six consecutive days.
- Use statistical methods to interpret the data and draw conclusions regarding the variability and consistency of the caffeine content in the coffee blend.

**Note:**
This data can be utilized for various statistical analyses such as calculating the mean, median, mode, range, and standard deviation to understand the dispersion and central tendency of the caffeine content in the coffee samples.

### Hypothesis Testing for Median Caffeine Content

#### a. Formulating the Hypotheses
Suppose the scientists are interested in determining whether the median amount of caffeine in this coffee blend exceeds 325 milligrams. Set up the null and alternative hypotheses of interest:

- Null Hypothesis (H₀): η = 325
- Alternative Hypothesis (Hₐ): η > 325

#### b. Sample Analysis
How many of the cups in the sample have a caffeine content that exceeds 325 milligrams?

- **Answer:** 5 cups

#### c. Probability Calculation
Assuming that p = 0.5, find the probability that at least as many of the 6 cups as were counted in part (b) have caffeine amounts that exceed 325 milligrams.

- **Answer:** The probability is 0.031 (rounded to three decimal places as needed).

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