On average, Americans have lived in 2 places by the time they are 18 years old. Is this average less for college students? The 62 randomly selected college students who answered the survey question had lived in an average of 1.99 places by the time they were 18 years old. The standard deviation for the survey group was 0.3. What can be concluded at the a = 0.10 level of significance? a. For this study, we should use t-test for a population mean b. The null and alternative hypotheses would be:
On average, Americans have lived in 2 places by the time they are 18 years old. Is this average less for college students? The 62 randomly selected college students who answered the survey question had lived in an average of 1.99 places by the time they were 18 years old. The standard deviation for the survey group was 0.3. What can be concluded at the a = 0.10 level of significance? a. For this study, we should use t-test for a population mean b. The null and alternative hypotheses would be:
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
help with B C AND D ONLY PLEASE
![### Statistical Hypothesis Testing Example
**Scenario:**
On average, Americans have lived in 2 places by the time they are 18 years old. Is this average less for college students?
To investigate, 62 randomly selected college students who answered the survey question had lived in an average of 1.99 places by the time they were 18 years old. The standard deviation for the survey group was 0.3. We will conclude based on the \( \alpha = 0.10 \) level of significance.
**Procedure:**
a. **Selecting the appropriate test:**
For this study, we should use:
- **t-test for a population mean**
b. **Formulating hypotheses:**
The null and alternative hypotheses would be:
- \( H_0 \): \( \mu \geq 2 \) (The average number of places for college students is not less than 2)
- \( H_1 \): \( \mu < 2 \) (The average number of places for college students is less than 2)
c. **Calculating the test statistic:**
The formula for the t-test statistic is:
\[
t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}
\]
where:
- \( \bar{x} \) = sample mean = 1.99
- \( \mu_0 \) = population mean = 2
- \( s \) = standard deviation = 0.3
- \( n \) = sample size = 62
Substitute these values into the formula to calculate the t statistic:
\[
t = \frac{1.99 - 2}{0.3 / \sqrt{62}}
\]
(please show your answer to 3 decimal places.)
d. **Finding the p-value:**
The p-value is found using the t distribution table or statistical software.
- (Please show your answer to 4 decimal places.)
By comparing the p-value to the alpha level, we can determine whether to reject or fail to reject the null hypothesis.
**Note:**
The "Select an answer" dropdowns and blank boxes are meant for students to fill in their answers during the exercise. Statistical software or a t-distribution table is typically used to calculate the exact values](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2d30e49-de0d-418d-b702-a4b3e53b4c91%2F92d63493-c79e-442e-b9b0-1df365eb247e%2Fb30rjdj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Statistical Hypothesis Testing Example
**Scenario:**
On average, Americans have lived in 2 places by the time they are 18 years old. Is this average less for college students?
To investigate, 62 randomly selected college students who answered the survey question had lived in an average of 1.99 places by the time they were 18 years old. The standard deviation for the survey group was 0.3. We will conclude based on the \( \alpha = 0.10 \) level of significance.
**Procedure:**
a. **Selecting the appropriate test:**
For this study, we should use:
- **t-test for a population mean**
b. **Formulating hypotheses:**
The null and alternative hypotheses would be:
- \( H_0 \): \( \mu \geq 2 \) (The average number of places for college students is not less than 2)
- \( H_1 \): \( \mu < 2 \) (The average number of places for college students is less than 2)
c. **Calculating the test statistic:**
The formula for the t-test statistic is:
\[
t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}
\]
where:
- \( \bar{x} \) = sample mean = 1.99
- \( \mu_0 \) = population mean = 2
- \( s \) = standard deviation = 0.3
- \( n \) = sample size = 62
Substitute these values into the formula to calculate the t statistic:
\[
t = \frac{1.99 - 2}{0.3 / \sqrt{62}}
\]
(please show your answer to 3 decimal places.)
d. **Finding the p-value:**
The p-value is found using the t distribution table or statistical software.
- (Please show your answer to 4 decimal places.)
By comparing the p-value to the alpha level, we can determine whether to reject or fail to reject the null hypothesis.
**Note:**
The "Select an answer" dropdowns and blank boxes are meant for students to fill in their answers during the exercise. Statistical software or a t-distribution table is typically used to calculate the exact values
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 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