MATLAB: An Introduction with Applications
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Author: Amos Gilat
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need part c please. and how to do it in the future myself
![### Hypothesis Testing: Statistical Decision Example
**Scenario:**
In a sample of \( n = 16 \) selected from a normal population, with \( \bar{X} = 55 \) and \( S = 12 \), determine the statistical decision if the level of significance, \( \alpha \), is 0.01. The null hypothesis, \( H_0 \), is \( \mu = 50 \), and the alternative hypothesis, \( H_1 \), is \( \mu \neq 50 \).
**Critical Values Determination:**
The critical value(s) for this test are \( -2.9467, 2.9467 \).
*(Round to four decimal places as needed. Use a comma to separate answers as needed.)*
**Test Statistic Calculation:**
Calculate the test statistic, \( t_{\text{STAT}} \):
\[ t_{\text{STAT}} = 1.6667 \]
*(Round to four decimal places as needed.)*
**Statistical Decision:**
Choose the correct statistical decision below:
- **A.** The test does not reject the null hypothesis. The data provide sufficient evidence to conclude that the mean differs from \( \mu = 50 \).
- **B.** The test rejects the null hypothesis. The data does not provide sufficient evidence to conclude that the mean differs from \( \mu = 50 \).
- **C.** The test rejects the null hypothesis. The data provide sufficient evidence to conclude that the mean differs from \( \mu = 50 \).
- **D.** The test does not reject the null hypothesis. The data does not provide sufficient evidence to conclude that the mean differs from \( \mu = 50 \).](https://content.bartleby.com/qna-images/question/364ff841-973c-4adc-ac42-2ffc3e4d2725/0846ac2a-9fa7-485f-8b52-e60439bf9348/6hmp8t_processed.png)
Transcribed Image Text:### Hypothesis Testing: Statistical Decision Example
**Scenario:**
In a sample of \( n = 16 \) selected from a normal population, with \( \bar{X} = 55 \) and \( S = 12 \), determine the statistical decision if the level of significance, \( \alpha \), is 0.01. The null hypothesis, \( H_0 \), is \( \mu = 50 \), and the alternative hypothesis, \( H_1 \), is \( \mu \neq 50 \).
**Critical Values Determination:**
The critical value(s) for this test are \( -2.9467, 2.9467 \).
*(Round to four decimal places as needed. Use a comma to separate answers as needed.)*
**Test Statistic Calculation:**
Calculate the test statistic, \( t_{\text{STAT}} \):
\[ t_{\text{STAT}} = 1.6667 \]
*(Round to four decimal places as needed.)*
**Statistical Decision:**
Choose the correct statistical decision below:
- **A.** The test does not reject the null hypothesis. The data provide sufficient evidence to conclude that the mean differs from \( \mu = 50 \).
- **B.** The test rejects the null hypothesis. The data does not provide sufficient evidence to conclude that the mean differs from \( \mu = 50 \).
- **C.** The test rejects the null hypothesis. The data provide sufficient evidence to conclude that the mean differs from \( \mu = 50 \).
- **D.** The test does not reject the null hypothesis. The data does not provide sufficient evidence to conclude that the mean differs from \( \mu = 50 \).
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