At a large university, 80% of all students live on campus. Suppose a random selected from this university and the sample proportion is defined as the p sample who live on campus. Determine the mean of the sampling distribut 0 0.95 0 0.8
At a large university, 80% of all students live on campus. Suppose a random selected from this university and the sample proportion is defined as the p sample who live on campus. Determine the mean of the sampling distribut 0 0.95 0 0.8
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
#21).
![### Example Problem on Sampling Distribution
#### Problem Statement:
At a large university, 80% of all students live on campus. Suppose a random sample of 218 students is selected from this university and the sample proportion is defined as the proportion of students in the sample who live on campus. Determine the mean of the sampling distribution of \( \hat{p} \).
#### Answer Choices:
- ○ 0.95
- ○ 0.8
- ○ 0.2
- ○ 0.35
#### Explanation:
To calculate the mean of the sampling distribution of \( \hat{p} \) (which is the sample proportion), we use the fact that the mean of the sampling distribution of \( \hat{p} \) is equal to the population proportion \( p \).
Given that the population proportion \( p \) is 0.80 (or 80%), the mean of the sampling distribution of \( \hat{p} \) is:
\[ \text{Mean of } \hat{p} = p = 0.8 \]
Therefore, the correct answer is:
- ○ 0.8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc94cb5d1-997a-49d0-b0ef-9ec02bf0a187%2F5e7bcab7-4e37-4932-bc4a-4de6636e0b38%2F2jpagcw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Example Problem on Sampling Distribution
#### Problem Statement:
At a large university, 80% of all students live on campus. Suppose a random sample of 218 students is selected from this university and the sample proportion is defined as the proportion of students in the sample who live on campus. Determine the mean of the sampling distribution of \( \hat{p} \).
#### Answer Choices:
- ○ 0.95
- ○ 0.8
- ○ 0.2
- ○ 0.35
#### Explanation:
To calculate the mean of the sampling distribution of \( \hat{p} \) (which is the sample proportion), we use the fact that the mean of the sampling distribution of \( \hat{p} \) is equal to the population proportion \( p \).
Given that the population proportion \( p \) is 0.80 (or 80%), the mean of the sampling distribution of \( \hat{p} \) is:
\[ \text{Mean of } \hat{p} = p = 0.8 \]
Therefore, the correct answer is:
- ○ 0.8
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