Overtime Hours Worked A random sample of 18 registered nurses in a large hospital showed that they worked on average 44.9 hours per week. The standard devlation of the sample was 2.6. Estimate the mean of the population with 90% confidence. Assume the variable is normally distributed. Round Intermedlate answers to at least three decimal places. Round your final answers to one decimal place. くpく

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
**Overtime Hours Worked**

A random sample of 18 registered nurses in a large hospital showed that they worked on average 44.9 hours per week. The standard deviation of the sample was 2.6. Estimate the mean of the population with 90% confidence. Assume the variable is normally distributed. Round intermediate answers to at least three decimal places. Round your final answers to one decimal place.

Below this text, there is a diagram representing the structure of the confidence interval for the mean:

\[ \text{Illustration of the range} < \mu < \text{Illustration of the range} \]

In the diagram, \( \overline{X} \) represents the sample mean and \( S \) represents the standard deviation. 

**Calculation Steps:**

1. **Determine the Sample Mean (\( \overline{X} \)):**
   The sample mean provided is 44.9 hours.

2. **Standard Deviation (S):**
   The standard deviation provided is 2.6 hours.

3. **Sample Size (n):**
   The sample size is 18.

4. **Confidence Level:**
   The desired confidence level is 90%.

The rest of the page may involve the mathematical process to determine the confidence interval, using the t-distribution due to the small sample size (n < 30).

Click on "Check" after calculating to verify your answer.

Options for actions include "Save For Later" and "Submit Assignment." 

For more detailed steps and explanations for constructing a confidence interval, consult the statistical section of our educational resources.
Transcribed Image Text:**Overtime Hours Worked** A random sample of 18 registered nurses in a large hospital showed that they worked on average 44.9 hours per week. The standard deviation of the sample was 2.6. Estimate the mean of the population with 90% confidence. Assume the variable is normally distributed. Round intermediate answers to at least three decimal places. Round your final answers to one decimal place. Below this text, there is a diagram representing the structure of the confidence interval for the mean: \[ \text{Illustration of the range} < \mu < \text{Illustration of the range} \] In the diagram, \( \overline{X} \) represents the sample mean and \( S \) represents the standard deviation. **Calculation Steps:** 1. **Determine the Sample Mean (\( \overline{X} \)):** The sample mean provided is 44.9 hours. 2. **Standard Deviation (S):** The standard deviation provided is 2.6 hours. 3. **Sample Size (n):** The sample size is 18. 4. **Confidence Level:** The desired confidence level is 90%. The rest of the page may involve the mathematical process to determine the confidence interval, using the t-distribution due to the small sample size (n < 30). Click on "Check" after calculating to verify your answer. Options for actions include "Save For Later" and "Submit Assignment." For more detailed steps and explanations for constructing a confidence interval, consult the statistical section of our educational resources.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Point Estimation, Limit Theorems, Approximations, and Bounds
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman