Use the formula Ỹ - to.05(2),df SE < μ< Ỹ + 10.05(2),df SE to calculate a 95% confidence interval for mean sleep time in the cave population. In the formula, μ is the population mean, Y is he sample mean, to.05(2),df is a two-tailed critical value of the t-distribution with df degrees of freedom, and SE is the standard error of the mean. Use Statistical Table C if necessary. Give your answer as an interval in the form (lower bound, upper bound). Round each of the bounds to one decimal place.
Use the formula Ỹ - to.05(2),df SE < μ< Ỹ + 10.05(2),df SE to calculate a 95% confidence interval for mean sleep time in the cave population. In the formula, μ is the population mean, Y is he sample mean, to.05(2),df is a two-tailed critical value of the t-distribution with df degrees of freedom, and SE is the standard error of the mean. Use Statistical Table C if necessary. Give your answer as an interval in the form (lower bound, upper bound). Round each of the bounds to one decimal place.
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
please answer!
![The evolution of blind cave forms of the fish *Astyanax mexicanus* is associated with large reductions in the amount of time spent sleeping. The eyed, surface forms sleep about 800 minutes per 24-hour day (about 13 hours). The accompanying graph shows the frequency distribution of sleep times per 24 hours for 23 blind individuals from a single cave population (Duboué et al. 2011). The sample mean is 129.4 and the standard deviation is 147.2. Assume that the sample is a random sample.
### Graph Explanation
A histogram illustrates the frequency distribution of sleep times:
- **Time sleeping (min):**
- 0-100 minutes: Frequency of 10
- 100-200 minutes: Frequency of 3
- 200-300 minutes: Frequency of 3
- 300-400 minutes: Frequency of 3
- 400-500 minutes: Frequency of 4
### Statistical Analysis
Use the formula:
\[
\bar{Y} - t_{0.05(2),df} \frac{SE_{\bar{Y}}}{\ } < \mu < \bar{Y} + t_{0.05(2),df} \frac{SE_{\bar{Y}}}{\ }
\]
to calculate a 95% confidence interval for the mean sleep time in the cave population. In the formula:
- \(\mu\) is the population mean,
- \(\bar{Y}\) is the sample mean,
- \(t_{0.05(2),df}\) is a two-tailed critical value of the *t*-distribution with *df* degrees of freedom,
- \(SE_{\bar{Y}}\) is the standard error of the mean.
Use [Statistical Table C](#) if necessary.
### Instructions
Give your answer as an interval in the form (lower bound, upper bound). Round each of the bounds to one decimal place.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa451162e-14ac-4cfd-a2c6-1eae7f4a5f1a%2F9ef923a3-16b3-4e2a-8918-52c33560fa95%2Frm0hzi_processed.png&w=3840&q=75)
Transcribed Image Text:The evolution of blind cave forms of the fish *Astyanax mexicanus* is associated with large reductions in the amount of time spent sleeping. The eyed, surface forms sleep about 800 minutes per 24-hour day (about 13 hours). The accompanying graph shows the frequency distribution of sleep times per 24 hours for 23 blind individuals from a single cave population (Duboué et al. 2011). The sample mean is 129.4 and the standard deviation is 147.2. Assume that the sample is a random sample.
### Graph Explanation
A histogram illustrates the frequency distribution of sleep times:
- **Time sleeping (min):**
- 0-100 minutes: Frequency of 10
- 100-200 minutes: Frequency of 3
- 200-300 minutes: Frequency of 3
- 300-400 minutes: Frequency of 3
- 400-500 minutes: Frequency of 4
### Statistical Analysis
Use the formula:
\[
\bar{Y} - t_{0.05(2),df} \frac{SE_{\bar{Y}}}{\ } < \mu < \bar{Y} + t_{0.05(2),df} \frac{SE_{\bar{Y}}}{\ }
\]
to calculate a 95% confidence interval for the mean sleep time in the cave population. In the formula:
- \(\mu\) is the population mean,
- \(\bar{Y}\) is the sample mean,
- \(t_{0.05(2),df}\) is a two-tailed critical value of the *t*-distribution with *df* degrees of freedom,
- \(SE_{\bar{Y}}\) is the standard error of the mean.
Use [Statistical Table C](#) if necessary.
### Instructions
Give your answer as an interval in the form (lower bound, upper bound). Round each of the bounds to one decimal place.
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 3 steps with 8 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