(1 point) In order to compare the means of two populations, independent random samples of 266 observations are selected from each population, with the following results: Sample 1 Sample 2 x1 = 1 x2 = 0 S1 = 105 s2 = 130 (a) Use a 97 % confidence interval to estimate the difference between the population means (µ1 – µ2). - -21.235 < (H1 – H2) < 23.235 (b) Test the null hypothesis: Ho : (µ1 – µ2) = 0 versus the alternative hypothesis: H. : (µj - H2) # 0. Using a = 0.03, give the following: (i) the test statistic z = (ii) the positive critical z score 2.176 (iii) the negative critical z score -2.176 The final conclustion is A. There is not sufficient evidence to reject the null hypothesis that (u1 – µ2) = 0. B. We can reject the null hypothesis that (u1 – µ2) = 0 and accept that (u1 – µ2) # 0. (c) Test the null hypothesis: Ho : (µ1 – µ2) = 21 versus the alternative hypothesis: H. : (µ1 - H2) # 21. Using a = 0.03, give the following: (i) the test statistic z = -1.952 (ii) the positive critical z score 2.176 (iii) the negative critical z score -2.176
(1 point) In order to compare the means of two populations, independent random samples of 266 observations are selected from each population, with the following results: Sample 1 Sample 2 x1 = 1 x2 = 0 S1 = 105 s2 = 130 (a) Use a 97 % confidence interval to estimate the difference between the population means (µ1 – µ2). - -21.235 < (H1 – H2) < 23.235 (b) Test the null hypothesis: Ho : (µ1 – µ2) = 0 versus the alternative hypothesis: H. : (µj - H2) # 0. Using a = 0.03, give the following: (i) the test statistic z = (ii) the positive critical z score 2.176 (iii) the negative critical z score -2.176 The final conclustion is A. There is not sufficient evidence to reject the null hypothesis that (u1 – µ2) = 0. B. We can reject the null hypothesis that (u1 – µ2) = 0 and accept that (u1 – µ2) # 0. (c) Test the null hypothesis: Ho : (µ1 – µ2) = 21 versus the alternative hypothesis: H. : (µ1 - H2) # 21. Using a = 0.03, give the following: (i) the test statistic z = -1.952 (ii) the positive critical z score 2.176 (iii) the negative critical z score -2.176
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![In order to compare the means of two populations, independent random samples of 266 observations are selected from each population, with the following results:
- **Sample 1:**
- \(\bar{x}_1 = 1\)
- \(s_1 = 105\)
- **Sample 2:**
- \(\bar{x}_2 = 0\)
- \(s_2 = 130\)
### (a) Use a 97% confidence interval to estimate the difference between the population means \((\mu_1 - \mu_2)\).
\[
-21.235 \leq (\mu_1 - \mu_2) \leq 23.235
\]
### (b) Test the null hypothesis:
\[
H_0 : (\mu_1 - \mu_2) = 0
\]
versus the alternative hypothesis:
\[
H_a : (\mu_1 - \mu_2) \neq 0
\]
Using \(\alpha = 0.03\), provide the following:
- (i) the test statistic \(z =\)
- (ii) the positive critical \(z\) score: \(2.176\)
- (iii) the negative critical \(z\) score: \(-2.176\)
**The final conclusion is:**
- **A. There is not sufficient evidence to reject the null hypothesis that \((\mu_1 - \mu_2) = 0\).**
- B. We can reject the null hypothesis that \((\mu_1 - \mu_2) = 0\) and accept that \((\mu_1 - \mu_2) \neq 0\).
### (c) Test the null hypothesis:
\[
H_0 : (\mu_1 - \mu_2) = 21
\]
versus the alternative hypothesis:
\[
H_a : (\mu_1 - \mu_2) \neq 21
\]
Using \(\alpha = 0.03\), provide the following:
- (i) the test statistic \(z = -1.952\)
- (ii) the positive critical \(z\) score: \(2.176\)
- (iii) the negative critical \(z\) score: \(-2.176\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04c10408-5cfd-4d68-aa09-84e3c4534233%2F87d34459-65fb-4459-9418-d10d0806f826%2F30jb5gh_processed.png&w=3840&q=75)
Transcribed Image Text:In order to compare the means of two populations, independent random samples of 266 observations are selected from each population, with the following results:
- **Sample 1:**
- \(\bar{x}_1 = 1\)
- \(s_1 = 105\)
- **Sample 2:**
- \(\bar{x}_2 = 0\)
- \(s_2 = 130\)
### (a) Use a 97% confidence interval to estimate the difference between the population means \((\mu_1 - \mu_2)\).
\[
-21.235 \leq (\mu_1 - \mu_2) \leq 23.235
\]
### (b) Test the null hypothesis:
\[
H_0 : (\mu_1 - \mu_2) = 0
\]
versus the alternative hypothesis:
\[
H_a : (\mu_1 - \mu_2) \neq 0
\]
Using \(\alpha = 0.03\), provide the following:
- (i) the test statistic \(z =\)
- (ii) the positive critical \(z\) score: \(2.176\)
- (iii) the negative critical \(z\) score: \(-2.176\)
**The final conclusion is:**
- **A. There is not sufficient evidence to reject the null hypothesis that \((\mu_1 - \mu_2) = 0\).**
- B. We can reject the null hypothesis that \((\mu_1 - \mu_2) = 0\) and accept that \((\mu_1 - \mu_2) \neq 0\).
### (c) Test the null hypothesis:
\[
H_0 : (\mu_1 - \mu_2) = 21
\]
versus the alternative hypothesis:
\[
H_a : (\mu_1 - \mu_2) \neq 21
\]
Using \(\alpha = 0.03\), provide the following:
- (i) the test statistic \(z = -1.952\)
- (ii) the positive critical \(z\) score: \(2.176\)
- (iii) the negative critical \(z\) score: \(-2.176\)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman