Consider the hypothesis test Ho: M₁ = sizes n₁ = 9 and n₂ = 15 and that x₁ = (a) Test the hypothesis and find the P-value. 2 against H₁₁ < 2 with known variances 0₁ = 9 and ₂ = 5. Suppose that sample 14.3 and ₂ = 19.5. Use a = 0.05. (b) What is the power of the test in part (a) if μ₁ is 4 units less than μ₂? (c) Assuming equal sample sizes, what sample size should be used to obtain ß = 0.05 if μ₁ is 4 units less than μ₂? Assume that a = 0.05. (a) The null hypothesis (e.g. 98.7654). (b) The power is i (c) n₁ = n₂ = ✓rejected. The P-value is i . Round your answer to four decimal places . Round your answer to two decimal places (e.g. 98.76). Round your answer up to the nearest integer. Statistical Tables and Charts
Consider the hypothesis test Ho: M₁ = sizes n₁ = 9 and n₂ = 15 and that x₁ = (a) Test the hypothesis and find the P-value. 2 against H₁₁ < 2 with known variances 0₁ = 9 and ₂ = 5. Suppose that sample 14.3 and ₂ = 19.5. Use a = 0.05. (b) What is the power of the test in part (a) if μ₁ is 4 units less than μ₂? (c) Assuming equal sample sizes, what sample size should be used to obtain ß = 0.05 if μ₁ is 4 units less than μ₂? Assume that a = 0.05. (a) The null hypothesis (e.g. 98.7654). (b) The power is i (c) n₁ = n₂ = ✓rejected. The P-value is i . Round your answer to four decimal places . Round your answer to two decimal places (e.g. 98.76). Round your answer up to the nearest integer. Statistical Tables and Charts
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 Exercise
Consider the hypothesis test \( H_0: \mu_1 = \mu_2 \) against \( H_1: \mu_1 < \mu_2 \) with known variances \( \sigma_1 = 9 \) and \( \sigma_2 = 5 \). Given:
- Sample sizes: \( n_1 = 9 \) and \( n_2 = 15 \)
- Sample means: \( \bar{x}_1 = 14.3 \) and \( \bar{x}_2 = 19.5 \)
- Significance level: \( \alpha = 0.05 \)
### Questions:
(a) **Test the Hypothesis and Find the P-Value:**
- Determine if the null hypothesis should be rejected or not.
- Calculate the P-value and round your answer to four decimal places.
(b) **Calculate the Power of the Test:**
- What is the power of the test if \( \mu_1 \) is 4 units less than \( \mu_2 \)?
- Round your answer to two decimal places.
(c) **Determine the Required Sample Size for a Given Power:**
- Assuming equal sample sizes, calculate the sample size required to achieve a power level \( \beta = 0.05 \) if \( \mu_1 \) is 4 units less than \( \mu_2 \).
- Round your answer to the nearest integer.
### Entry Fields:
1. **(a) The null hypothesis**: [Dropdown: rejected | not rejected]
2. **P-value**: [Input field, e.g., 98.7654]
3. **(b) The power is**: [Input field, rounded to two decimals, e.g., 98.76]
4. **(c) \( n_1 = n_2 = \)**: [Input field, round to nearest integer]
### Additional Resources:
For assistance with statistical calculations, refer to the [Statistical Tables and Charts] link.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00114bb1-0365-4dfa-83cb-10b10c9a61b0%2F0db58ecb-791f-4a16-a3d4-d6234f10585b%2Fg4yvpyh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Hypothesis Testing Exercise
Consider the hypothesis test \( H_0: \mu_1 = \mu_2 \) against \( H_1: \mu_1 < \mu_2 \) with known variances \( \sigma_1 = 9 \) and \( \sigma_2 = 5 \). Given:
- Sample sizes: \( n_1 = 9 \) and \( n_2 = 15 \)
- Sample means: \( \bar{x}_1 = 14.3 \) and \( \bar{x}_2 = 19.5 \)
- Significance level: \( \alpha = 0.05 \)
### Questions:
(a) **Test the Hypothesis and Find the P-Value:**
- Determine if the null hypothesis should be rejected or not.
- Calculate the P-value and round your answer to four decimal places.
(b) **Calculate the Power of the Test:**
- What is the power of the test if \( \mu_1 \) is 4 units less than \( \mu_2 \)?
- Round your answer to two decimal places.
(c) **Determine the Required Sample Size for a Given Power:**
- Assuming equal sample sizes, calculate the sample size required to achieve a power level \( \beta = 0.05 \) if \( \mu_1 \) is 4 units less than \( \mu_2 \).
- Round your answer to the nearest integer.
### Entry Fields:
1. **(a) The null hypothesis**: [Dropdown: rejected | not rejected]
2. **P-value**: [Input field, e.g., 98.7654]
3. **(b) The power is**: [Input field, rounded to two decimals, e.g., 98.76]
4. **(c) \( n_1 = n_2 = \)**: [Input field, round to nearest integer]
### Additional Resources:
For assistance with statistical calculations, refer to the [Statistical Tables and Charts] link.
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