MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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The second box options are so not reject & reject the third box options are is not and is. Pls help
i need in an hour Thankyou.
![**Statistical Analysis of Baseball Player Heights**
**Background:**
Data show that men between the ages of 20 and 29 in a general population have a mean height of 69.3 inches, with a standard deviation of 2.9 inches. A baseball analyst is interested to know whether the standard deviation of heights of major-league baseball players is less than 2.9 inches. The heights (in inches) of 20 randomly selected players are provided in the accompanying table.
**Data Table:**
Heights of 20 randomly selected baseball players are:
- 72, 74, 71, 72, 76
- 70, 77, 75, 72, 72
- 77, 70, 75, 76, 73
- 74, 75, 73, 74, 74
**Hypothesis Testing:**
1. **Test Notion:**
- Significance Level: \(\alpha = 0.10\).
2. **Hypotheses:**
- Null Hypothesis (\(H_0\)): \(\sigma = 2.9\)
- Alternative Hypothesis (\(H_1\)): \(\sigma < 2.9\)
3. **Test Statistic:**
- Calculate the value of the test statistic using the formula for the chi-square test for standard deviation:
\[
X^2 = \frac{(n-1)s^2}{\sigma^2}
\]
- Round the result to three decimal places as needed.
4. **P-value:**
- Utilize technology or statistical software to compute the P-value corresponding to the chi-square test statistic.
- Round to three decimal places.
5. **Conclusion:**
- Compare the P-value with \(\alpha = 0.10\).
- If the P-value is less than \(\alpha\), reject the null hypothesis, indicating there is sufficient evidence to conclude that the standard deviation of heights of major-league baseball players is less than 2.9 inches.
- Otherwise, do not reject the null hypothesis.
**Graphical Explanation:**
- The image includes a data table featuring the heights of 20 players and spaces for inserting statistical results (test statistic, P-value) alongside a dropdown to select comparative symbols and make a conclusion regarding the hypothesis test.
- The interface supports interactive elements,](https://content.bartleby.com/qna-images/question/740a4bca-4536-466f-8fb5-22c7f56f9691/cc023b66-8c8c-4c9c-8c60-8dd0d452f062/9yr73qq5_processed.jpeg)
Transcribed Image Text:**Statistical Analysis of Baseball Player Heights**
**Background:**
Data show that men between the ages of 20 and 29 in a general population have a mean height of 69.3 inches, with a standard deviation of 2.9 inches. A baseball analyst is interested to know whether the standard deviation of heights of major-league baseball players is less than 2.9 inches. The heights (in inches) of 20 randomly selected players are provided in the accompanying table.
**Data Table:**
Heights of 20 randomly selected baseball players are:
- 72, 74, 71, 72, 76
- 70, 77, 75, 72, 72
- 77, 70, 75, 76, 73
- 74, 75, 73, 74, 74
**Hypothesis Testing:**
1. **Test Notion:**
- Significance Level: \(\alpha = 0.10\).
2. **Hypotheses:**
- Null Hypothesis (\(H_0\)): \(\sigma = 2.9\)
- Alternative Hypothesis (\(H_1\)): \(\sigma < 2.9\)
3. **Test Statistic:**
- Calculate the value of the test statistic using the formula for the chi-square test for standard deviation:
\[
X^2 = \frac{(n-1)s^2}{\sigma^2}
\]
- Round the result to three decimal places as needed.
4. **P-value:**
- Utilize technology or statistical software to compute the P-value corresponding to the chi-square test statistic.
- Round to three decimal places.
5. **Conclusion:**
- Compare the P-value with \(\alpha = 0.10\).
- If the P-value is less than \(\alpha\), reject the null hypothesis, indicating there is sufficient evidence to conclude that the standard deviation of heights of major-league baseball players is less than 2.9 inches.
- Otherwise, do not reject the null hypothesis.
**Graphical Explanation:**
- The image includes a data table featuring the heights of 20 players and spaces for inserting statistical results (test statistic, P-value) alongside a dropdown to select comparative symbols and make a conclusion regarding the hypothesis test.
- The interface supports interactive elements,
![**Statistical Analysis of Baseball Players' Heights**
Data shows that men between the ages of 20 and 29 in a general population have a mean height of 69.3 inches, with a standard deviation of 2.9 inches. A baseball analyst is questioning whether the standard deviation of the heights of major league baseball players is less than 2.9 inches. The heights (in inches) of 20 randomly selected players are displayed in the data table.
**Data Table:**
- Heights: 72, 74, 71, 72, 76, 70, 77, 75, 72, 72, 77, 72, 70, 73, 74, 74, 75, 73, 74
**Hypothesis Testing at α = 0.10 Level of Significance**
1. **Hypotheses:**
- Null Hypothesis (H₀): σ ≥ 2.9
- Alternative Hypothesis (Hₐ): σ < 2.9
2. **Calculate the Test Statistic:**
- Use the formula to compute the test statistic (χ²).
- Round the result to three decimal places.
3. **Determine the P-value:**
- Use technology or statistical software to find the P-value associated with the test statistic.
- Round the P-value to three decimal places.
4. **Conclusion:**
- Compare the P-value to the level of significance (α = 0.10).
- If the P-value is less than α, reject the null hypothesis.
- If the P-value is greater than α, do not reject the null hypothesis.
**Conclusion at α = 0.10:**
- Since the P-value is [less/greater] than the level of significance, [reject/do not reject] the null hypothesis. There is [sufficient/insufficient] evidence to conclude that the standard deviation of the heights of major league baseball players is less than 2.9 inches at the 0.10 level of significance.](https://content.bartleby.com/qna-images/question/740a4bca-4536-466f-8fb5-22c7f56f9691/cc023b66-8c8c-4c9c-8c60-8dd0d452f062/l0akytq_processed.jpeg)
Transcribed Image Text:**Statistical Analysis of Baseball Players' Heights**
Data shows that men between the ages of 20 and 29 in a general population have a mean height of 69.3 inches, with a standard deviation of 2.9 inches. A baseball analyst is questioning whether the standard deviation of the heights of major league baseball players is less than 2.9 inches. The heights (in inches) of 20 randomly selected players are displayed in the data table.
**Data Table:**
- Heights: 72, 74, 71, 72, 76, 70, 77, 75, 72, 72, 77, 72, 70, 73, 74, 74, 75, 73, 74
**Hypothesis Testing at α = 0.10 Level of Significance**
1. **Hypotheses:**
- Null Hypothesis (H₀): σ ≥ 2.9
- Alternative Hypothesis (Hₐ): σ < 2.9
2. **Calculate the Test Statistic:**
- Use the formula to compute the test statistic (χ²).
- Round the result to three decimal places.
3. **Determine the P-value:**
- Use technology or statistical software to find the P-value associated with the test statistic.
- Round the P-value to three decimal places.
4. **Conclusion:**
- Compare the P-value to the level of significance (α = 0.10).
- If the P-value is less than α, reject the null hypothesis.
- If the P-value is greater than α, do not reject the null hypothesis.
**Conclusion at α = 0.10:**
- Since the P-value is [less/greater] than the level of significance, [reject/do not reject] the null hypothesis. There is [sufficient/insufficient] evidence to conclude that the standard deviation of the heights of major league baseball players is less than 2.9 inches at the 0.10 level of significance.
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