To test Ho: o=2.8 versus H₁: <2.8, a random sample of size n = 21 is obtained from a population that is known to be normally distributed. H (a) If the sample standard deviation is determined to be s=1.3, compute the test statistic. x= 4.311 (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the a=0.10 level of significance, determine the critical value. The critical value is (Round to three decimal places as needed.)
To test Ho: o=2.8 versus H₁: <2.8, a random sample of size n = 21 is obtained from a population that is known to be normally distributed. H (a) If the sample standard deviation is determined to be s=1.3, compute the test statistic. x= 4.311 (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the a=0.10 level of significance, determine the critical value. The critical value is (Round to three decimal places as needed.)
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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![### Hypothesis Testing for Population Standard Deviation
To test \( H_0: \sigma = 2.8 \) versus \( H_1: \sigma < 2.8 \), a random sample of size \( n = 21 \) is obtained from a population that is known to be normally distributed.
#### (a) Test Statistic Calculation
If the sample standard deviation is determined to be \( s = 1.3 \), compute the test statistic using the formula:
\[
\chi_0^2 = \frac{(n-1)s^2}{\sigma_0^2}
\]
- \( n = 21 \)
- \( s = 1.3 \)
- \( \sigma_0 = 2.8 \)
Substitute these values into the formula:
\[
\chi_0^2 = \frac{(21-1)(1.3)^2}{(2.8)^2} = 4.311
\]
(Round to three decimal places as needed.)
#### (b) Determining the Critical Value
If the researcher decides to test this hypothesis at the \( \alpha = 0.10 \) level of significance, determine the critical value.
The critical value is \( \chi_{\alpha}^2 = \) [value to be filled in] \( \). (Round to three decimal places as needed.)
### Example Calculations and Further Assistance
- **Help me solve this**: Get guided step-by-step solutions for similar problems.
- **View an example**: Look at example problems with complete solutions.
- **Get more help**: Access additional resources and tutorials for more practice and understanding.
#### Notes:
- Ensure to use the chi-squared distribution table to find the critical value corresponding to \( \alpha = 0.10 \) for \( \nu = n - 1 \) degrees of freedom.
- Always round your final computed values to three decimal places unless instructed otherwise.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2241529c-3605-4343-8b09-279b4f80df33%2Fcf006e1b-ebcc-4d3d-a0c8-316b7136c8de%2F7k2v4n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for Population Standard Deviation
To test \( H_0: \sigma = 2.8 \) versus \( H_1: \sigma < 2.8 \), a random sample of size \( n = 21 \) is obtained from a population that is known to be normally distributed.
#### (a) Test Statistic Calculation
If the sample standard deviation is determined to be \( s = 1.3 \), compute the test statistic using the formula:
\[
\chi_0^2 = \frac{(n-1)s^2}{\sigma_0^2}
\]
- \( n = 21 \)
- \( s = 1.3 \)
- \( \sigma_0 = 2.8 \)
Substitute these values into the formula:
\[
\chi_0^2 = \frac{(21-1)(1.3)^2}{(2.8)^2} = 4.311
\]
(Round to three decimal places as needed.)
#### (b) Determining the Critical Value
If the researcher decides to test this hypothesis at the \( \alpha = 0.10 \) level of significance, determine the critical value.
The critical value is \( \chi_{\alpha}^2 = \) [value to be filled in] \( \). (Round to three decimal places as needed.)
### Example Calculations and Further Assistance
- **Help me solve this**: Get guided step-by-step solutions for similar problems.
- **View an example**: Look at example problems with complete solutions.
- **Get more help**: Access additional resources and tutorials for more practice and understanding.
#### Notes:
- Ensure to use the chi-squared distribution table to find the critical value corresponding to \( \alpha = 0.10 \) for \( \nu = n - 1 \) degrees of freedom.
- Always round your final computed values to three decimal places unless instructed otherwise.
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