MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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State the null and alternative hypotheses, specify the test being used (i.e. two-tail one-sample Student’s t-test), report the results of the test (include the test statistic, p value, and whether or not you reject the null hypothesis), and relate your findings back to the questions being asked.  Below is a sample problem and answer.

### One-Tail, One-Sample Student’s t-Test on Vitamin D Levels

#### Descriptive Statistics

To analyze the vitamin D levels, I used a one-tail, one-sample Student’s t-test. The dataset includes the following vitamin D (Vit D) levels: 
- 405, 440, 380, 360, 375, 401, 390, 398, 357, 400, 369, 350, 404, 379, 385, 362, 378, 380, 359, 390 

Below is the table summarizing the descriptive statistics for each sample and Minitab output for the t-test results:

**Vitamin D Levels:**
- Mean: 383.10
- Standard Deviation (StDev): 21.45
- Standard Error (SE Mean): 4.80
- 95% Upper Bound for µ: 391.39
- Sample Size (N): 20

The given descriptive statistics table:

| N  | Mean | StDev | SE Mean | 95% Upper Bound for µ |
|----|------|-------|---------|----------------------|
| 20 | 383.10 | 21.45 | 4.80 | 391.39 |  

Note: \(\mu\) represents the mean of Vitamin D levels.

#### Test Results

**Hypotheses:**
- **Null hypothesis (H₀):** \(\mu = 400\)
- **Alternative hypothesis (H₁):** \(\mu < 400\)

Results output from the t-test:

| T-Value | P-Value |
|---------|----------|
| -3.52   | 0.001    |

The T-value of -3.52 and associated P-value < 0.001 indicates that we reject the null hypothesis that the sample mean \(\mu\) is equal to or greater than 400 IU. This suggests the sample mean is significantly less than 400 IU, prompting the manufacturer to investigate why production is resulting in inadequate doses.

### Problems to Do

1. **Pollutant Detection in Fish Liver**
    A certain enzyme in the liver of fish indicates trace amounts of a dangerous pollutant that is hard to detect chemically. Enzyme activities of less than 50 units per gram of liver indicate the presence of the pollutant. A random fish sample was taken from a stream
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Transcribed Image Text:### One-Tail, One-Sample Student’s t-Test on Vitamin D Levels #### Descriptive Statistics To analyze the vitamin D levels, I used a one-tail, one-sample Student’s t-test. The dataset includes the following vitamin D (Vit D) levels: - 405, 440, 380, 360, 375, 401, 390, 398, 357, 400, 369, 350, 404, 379, 385, 362, 378, 380, 359, 390 Below is the table summarizing the descriptive statistics for each sample and Minitab output for the t-test results: **Vitamin D Levels:** - Mean: 383.10 - Standard Deviation (StDev): 21.45 - Standard Error (SE Mean): 4.80 - 95% Upper Bound for µ: 391.39 - Sample Size (N): 20 The given descriptive statistics table: | N | Mean | StDev | SE Mean | 95% Upper Bound for µ | |----|------|-------|---------|----------------------| | 20 | 383.10 | 21.45 | 4.80 | 391.39 | Note: \(\mu\) represents the mean of Vitamin D levels. #### Test Results **Hypotheses:** - **Null hypothesis (H₀):** \(\mu = 400\) - **Alternative hypothesis (H₁):** \(\mu < 400\) Results output from the t-test: | T-Value | P-Value | |---------|----------| | -3.52 | 0.001 | The T-value of -3.52 and associated P-value < 0.001 indicates that we reject the null hypothesis that the sample mean \(\mu\) is equal to or greater than 400 IU. This suggests the sample mean is significantly less than 400 IU, prompting the manufacturer to investigate why production is resulting in inadequate doses. ### Problems to Do 1. **Pollutant Detection in Fish Liver** A certain enzyme in the liver of fish indicates trace amounts of a dangerous pollutant that is hard to detect chemically. Enzyme activities of less than 50 units per gram of liver indicate the presence of the pollutant. A random fish sample was taken from a stream
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