Two random samples were selected independently from populations having normal distributions. The statistics given below were extracted from the samples. Complete parts a through c. X₁ = 38.8 X₂ = 30.2 a. If o, 5 and o₂ =3 and the sample sizes are n₁ = 40 and n = 40, construct a 99% confidence interval for the difference between the two population means. The confidence interval is 6.23 s (H₁-H₂) ≤ 10.98 (Round to two decimal places as needed.) b. If o, 0₂, s, =5, and s₂ =3, and the sample sizes are n₁ = 20 and n., =20, construct a 99% confidence interval for the difference between the two population means. The confidence interval is ≤ (H₁-H₂) = (Round to two decimal places as needed.).
Two random samples were selected independently from populations having normal distributions. The statistics given below were extracted from the samples. Complete parts a through c. X₁ = 38.8 X₂ = 30.2 a. If o, 5 and o₂ =3 and the sample sizes are n₁ = 40 and n = 40, construct a 99% confidence interval for the difference between the two population means. The confidence interval is 6.23 s (H₁-H₂) ≤ 10.98 (Round to two decimal places as needed.) b. If o, 0₂, s, =5, and s₂ =3, and the sample sizes are n₁ = 20 and n., =20, construct a 99% confidence interval for the difference between the two population means. The confidence interval is ≤ (H₁-H₂) = (Round to two decimal places as needed.).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![## Comparing Two Population Means
Two random samples were independently selected from populations with normal distributions. The statistics extracted from these samples are as follows:
- Sample Mean 1 (\( \overline{x}_1 \)): 38.8
- Sample Mean 2 (\( \overline{x}_2 \)): 30.2
### Problems to Solve
#### a. Constructing a 99% Confidence Interval for the Difference between Two Population Means
Given the following information:
- Population standard deviation (σ) for the first sample (σ1): 5
- Population standard deviation (σ) for the second sample (σ2): 3
- Sample size for the first sample (n1): 40
- Sample size for the second sample (n2): 40
We aim to construct a 99% confidence interval for the difference between the two population means.
The confidence interval is calculated as:
\[ 6.23 < (\mu_1 - \mu_2) < 10.98 \]
**Note**: Values are rounded to two decimal places as needed.
#### b. Constructing Another 99% Confidence Interval
Given another set of information:
- Sample standard deviation (s) for the first sample (s1): 5
- Sample standard deviation (s) for the second sample (s2): 5
- Sample size for the first sample (n1): 20
- Sample size for the second sample (n2): 20
We aim to construct another 99% confidence interval for the difference between the two population means.
The confidence interval is calculated as:
\[ [ \ \ \ ] < (\mu_1 - \mu_2) < [ \ \ \ ] \]
**Note**: Values should be rounded to two decimal places as needed.
### Diagrams and Graphs
There are no diagrams or graphs associated with this text.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbdd081ff-4988-4514-ab5d-41964c228e08%2Fbbf5f0d6-42af-41f7-b156-7b6e42900551%2Fk5bo5wc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Comparing Two Population Means
Two random samples were independently selected from populations with normal distributions. The statistics extracted from these samples are as follows:
- Sample Mean 1 (\( \overline{x}_1 \)): 38.8
- Sample Mean 2 (\( \overline{x}_2 \)): 30.2
### Problems to Solve
#### a. Constructing a 99% Confidence Interval for the Difference between Two Population Means
Given the following information:
- Population standard deviation (σ) for the first sample (σ1): 5
- Population standard deviation (σ) for the second sample (σ2): 3
- Sample size for the first sample (n1): 40
- Sample size for the second sample (n2): 40
We aim to construct a 99% confidence interval for the difference between the two population means.
The confidence interval is calculated as:
\[ 6.23 < (\mu_1 - \mu_2) < 10.98 \]
**Note**: Values are rounded to two decimal places as needed.
#### b. Constructing Another 99% Confidence Interval
Given another set of information:
- Sample standard deviation (s) for the first sample (s1): 5
- Sample standard deviation (s) for the second sample (s2): 5
- Sample size for the first sample (n1): 20
- Sample size for the second sample (n2): 20
We aim to construct another 99% confidence interval for the difference between the two population means.
The confidence interval is calculated as:
\[ [ \ \ \ ] < (\mu_1 - \mu_2) < [ \ \ \ ] \]
**Note**: Values should be rounded to two decimal places as needed.
### Diagrams and Graphs
There are no diagrams or graphs associated with this text.
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