(1 point) Two independent samples have been selected, 95 observations from population 1 and 96 observations from population 2. The sample means have been calculated to be x = 10.6 and x2 and o; = 21. = 5.4. From previous experience with these populations, it is known that the variances are o? = 26 (a) Find o&-32)' answer: (b) Determine the rejection region for the test of Ho : (µ1 – H2) = 2.03 and Ha : (µ1 – µ2) > 2.03 Use a = 0.02. z > (c) Compute the test statistic.
(1 point) Two independent samples have been selected, 95 observations from population 1 and 96 observations from population 2. The sample means have been calculated to be x = 10.6 and x2 and o; = 21. = 5.4. From previous experience with these populations, it is known that the variances are o? = 26 (a) Find o&-32)' answer: (b) Determine the rejection region for the test of Ho : (µ1 – H2) = 2.03 and Ha : (µ1 – µ2) > 2.03 Use a = 0.02. z > (c) Compute the test statistic.
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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![**Two Independent Samples Hypothesis Testing**
*Context:*
Two independent samples have been selected, consisting of 95 observations from population 1 and 96 observations from population 2. The sample means have been calculated to be \( \bar{x}_1 = 10.6 \) and \( \bar{x}_2 = 5.4 \). From previous experience with these populations, it is known that the variances are \( \sigma^2_1 = 26 \) and \( \sigma^2_2 = 21 \).
**Tasks:**
(a) **Find the Standard Deviation \( \sigma_{\bar{x}_1 - \bar{x}_2} \).**
- **Answer:** [Insert calculation]
(b) **Determine the Rejection Region for the Hypothesis Test:**
- Null Hypothesis: \( H_0: (\mu_1 - \mu_2) = 2.03 \)
- Alternative Hypothesis: \( H_a: (\mu_1 - \mu_2) > 2.03 \)
- Significance Level: \( \alpha = 0.02 \)
- **Formula:** \( z > \) [Insert critical value]
(c) **Compute the Test Statistic.**
- **Formula for \( z \):**
- **Calculation:** \( z = \) [Insert computation]
**Final Conclusion:**
Choose one of the following:
- A. There is not sufficient evidence to reject the null hypothesis that \( (\mu_1 - \mu_2) = 2.03 \).
- B. We can reject the null hypothesis that \( (\mu_1 - \mu_2) = 2.03 \) and accept that \( (\mu_1 - \mu_2) > 2.03 \).
(d) **Construct a 98% Confidence Interval for \( (\mu_1 - \mu_2) \).**
- **Interval:** \( \leq (\mu_1 - \mu_2) \leq \)
- **Computation:** [Insert interval calculation]
Please complete the calculations using the appropriate statistical methods or software.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04c10408-5cfd-4d68-aa09-84e3c4534233%2F3d8e8c45-4693-4842-a6ef-08c7c37faf75%2Flx1r7l_processed.png&w=3840&q=75)
Transcribed Image Text:**Two Independent Samples Hypothesis Testing**
*Context:*
Two independent samples have been selected, consisting of 95 observations from population 1 and 96 observations from population 2. The sample means have been calculated to be \( \bar{x}_1 = 10.6 \) and \( \bar{x}_2 = 5.4 \). From previous experience with these populations, it is known that the variances are \( \sigma^2_1 = 26 \) and \( \sigma^2_2 = 21 \).
**Tasks:**
(a) **Find the Standard Deviation \( \sigma_{\bar{x}_1 - \bar{x}_2} \).**
- **Answer:** [Insert calculation]
(b) **Determine the Rejection Region for the Hypothesis Test:**
- Null Hypothesis: \( H_0: (\mu_1 - \mu_2) = 2.03 \)
- Alternative Hypothesis: \( H_a: (\mu_1 - \mu_2) > 2.03 \)
- Significance Level: \( \alpha = 0.02 \)
- **Formula:** \( z > \) [Insert critical value]
(c) **Compute the Test Statistic.**
- **Formula for \( z \):**
- **Calculation:** \( z = \) [Insert computation]
**Final Conclusion:**
Choose one of the following:
- A. There is not sufficient evidence to reject the null hypothesis that \( (\mu_1 - \mu_2) = 2.03 \).
- B. We can reject the null hypothesis that \( (\mu_1 - \mu_2) = 2.03 \) and accept that \( (\mu_1 - \mu_2) > 2.03 \).
(d) **Construct a 98% Confidence Interval for \( (\mu_1 - \mu_2) \).**
- **Interval:** \( \leq (\mu_1 - \mu_2) \leq \)
- **Computation:** [Insert interval calculation]
Please complete the calculations using the appropriate statistical methods or software.
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