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 3.2 inches. A baseball analyst wonders whether the standard deviation of heights of major-league baseball players is less than 3.2 inches. The heights (in inches) of 20 randomly selected players are shown in the table. E Click the icon to view the data table. Test the notion at the a = 0.01 level of significance. What are the correct hypotheses for this test? The null hypothesis is Ho: o = 3.2. The alternative hypothesis is H,: < 3.2. Data table Calculate the value of the test statistic. x2 = (Round to three decimal places as needed.) 72 74 71 71 76 70 77 76 72 72 77 | 71 | 7570 74 75 73 73 4 74
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 3.2 inches. A baseball analyst wonders whether the standard deviation of heights of major-league baseball players is less than 3.2 inches. The heights (in inches) of 20 randomly selected players are shown in the table. E Click the icon to view the data table. Test the notion at the a = 0.01 level of significance. What are the correct hypotheses for this test? The null hypothesis is Ho: o = 3.2. The alternative hypothesis is H,: < 3.2. Data table Calculate the value of the test statistic. x2 = (Round to three decimal places as needed.) 72 74 71 71 76 70 77 76 72 72 77 | 71 | 7570 74 75 73 73 4 74
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
Find Test Statistic, P value, and Z score.
![**Hypothesis Testing for Standard Deviation in Baseball Player Heights**
Data indicate that men aged 20 to 29 in a general population have a mean height of 69.3 inches, with a standard deviation of 3.2 inches. A baseball analyst is investigating if the standard deviation of heights for major-league baseball players is less than 3.2 inches. Heights (in inches) of 20 randomly selected players are provided.
**Objective:**
Test the hypothesis at a 0.01 level of significance.
**Hypotheses:**
- Null Hypothesis (H₀): σ = 3.2
- Alternative Hypothesis (H₁): σ < 3.2
**Data Table:**
The heights of the 20 sampled players are as follows:
| 72 | 74 | 71 | 71 | 76 |
|----|----|----|----|----|
| 70 | 77 | 76 | 72 | 72 |
| 77 | 71 | 75 | 70 | 73 |
| 74 | 75 | 73 | 74 | 74 |
**Task:**
Calculate the value of the test statistic:
\[ \chi^2 = \text{(Round to three decimal places as needed.)} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a558dc2-6562-462f-aa7a-976bc30edf62%2Ffae0a64a-f123-4b99-8576-d799aa00af50%2Fejeklem_processed.png&w=3840&q=75)
Transcribed Image Text:**Hypothesis Testing for Standard Deviation in Baseball Player Heights**
Data indicate that men aged 20 to 29 in a general population have a mean height of 69.3 inches, with a standard deviation of 3.2 inches. A baseball analyst is investigating if the standard deviation of heights for major-league baseball players is less than 3.2 inches. Heights (in inches) of 20 randomly selected players are provided.
**Objective:**
Test the hypothesis at a 0.01 level of significance.
**Hypotheses:**
- Null Hypothesis (H₀): σ = 3.2
- Alternative Hypothesis (H₁): σ < 3.2
**Data Table:**
The heights of the 20 sampled players are as follows:
| 72 | 74 | 71 | 71 | 76 |
|----|----|----|----|----|
| 70 | 77 | 76 | 72 | 72 |
| 77 | 71 | 75 | 70 | 73 |
| 74 | 75 | 73 | 74 | 74 |
**Task:**
Calculate the value of the test statistic:
\[ \chi^2 = \text{(Round to three decimal places as needed.)} \]
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