Suppose the manager of a restaurant in a commercial building has determined that the proportion of customers who drink tea is 24%. Based on a random sample of 250 customers, what is the standard error for the sampling distribution of the sample proportion of tea drinkers? 0.0427 0.0302 0.0247 0.0349 0.0270
Suppose the manager of a restaurant in a commercial building has determined that the proportion of customers who drink tea is 24%. Based on a random sample of 250 customers, what is the standard error for the sampling distribution of the sample proportion of tea drinkers? 0.0427 0.0302 0.0247 0.0349 0.0270
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
![**Sampling Distribution and Standard Error Calculation Example**
---
**Problem Description:**
Suppose the manager of a restaurant in a commercial building has determined that the proportion of customers who drink tea is 24%. Based on a random sample of 250 customers, what is the standard error for the sampling distribution of the sample proportion of tea drinkers?
**Answer Options:**
- \( \circ \) 0.0427
- \( \circ \) 0.0302
- \( \circ \) 0.0247
- \( \circ \) 0.0349
- \( \circ \) 0.0270
---
**Explanation:**
To find the standard error (SE) for the sampling distribution of the sample proportion, we use the following formula:
\[ \text{SE} = \sqrt{\frac{p(1-p)}{n}} \]
where:
- \( p \) is the population proportion (0.24 in this case)
- \( n \) is the sample size (250 in this case)
Plugging in the values:
\[ \text{SE} = \sqrt{\frac{0.24 \times (1 - 0.24)}{250}} \]
\[ \text{SE} = \sqrt{\frac{0.24 \times 0.76}{250}} \]
\[ \text{SE} = \sqrt{\frac{0.1824}{250}} \]
\[ \text{SE} = \sqrt{0.0007296} \]
\[ \text{SE} \approx 0.0270 \]
Therefore, the standard error for the sampling distribution of the sample proportion of tea drinkers is approximately 0.0270.
The correct answer is:
- \( \circ \) 0.0270
---
This calculation helps understand how much variability can be expected in the sample proportion due to sampling error when repeated samples are taken from the same population.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5018757-df34-47e5-8789-7c8e64b31b6d%2F9c75d7d0-d966-447d-bd2a-454e32348c90%2F6u5hu29_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Sampling Distribution and Standard Error Calculation Example**
---
**Problem Description:**
Suppose the manager of a restaurant in a commercial building has determined that the proportion of customers who drink tea is 24%. Based on a random sample of 250 customers, what is the standard error for the sampling distribution of the sample proportion of tea drinkers?
**Answer Options:**
- \( \circ \) 0.0427
- \( \circ \) 0.0302
- \( \circ \) 0.0247
- \( \circ \) 0.0349
- \( \circ \) 0.0270
---
**Explanation:**
To find the standard error (SE) for the sampling distribution of the sample proportion, we use the following formula:
\[ \text{SE} = \sqrt{\frac{p(1-p)}{n}} \]
where:
- \( p \) is the population proportion (0.24 in this case)
- \( n \) is the sample size (250 in this case)
Plugging in the values:
\[ \text{SE} = \sqrt{\frac{0.24 \times (1 - 0.24)}{250}} \]
\[ \text{SE} = \sqrt{\frac{0.24 \times 0.76}{250}} \]
\[ \text{SE} = \sqrt{\frac{0.1824}{250}} \]
\[ \text{SE} = \sqrt{0.0007296} \]
\[ \text{SE} \approx 0.0270 \]
Therefore, the standard error for the sampling distribution of the sample proportion of tea drinkers is approximately 0.0270.
The correct answer is:
- \( \circ \) 0.0270
---
This calculation helps understand how much variability can be expected in the sample proportion due to sampling error when repeated samples are taken from the same population.
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 3 steps with 3 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