Asked by Francielle Viana on Jun 06, 2024
Verified
In a local university, 70% of the students live in the dormitories.A random sample of 75 students is selected for a particular study.The standard deviation of , known as the standard error of the proportion is approximately
A) 0.5292.
B) 5.2915.
C) 0.0529.
D) 52.915.
Standard Error
A statistical measure that estimates the accuracy with which a sample distribution represents a population by using the standard deviation.
- Comprehend the principle and significance of standard error within the context of statistical inference.
- Comprehend the impact of differing probabilities on the standard error associated with proportions.
Verified Answer
SS
Shreelaxmi SahooJun 09, 2024
Final Answer :
C
Explanation :
The formula for the standard error of the proportion is:
SE = sqrt(p * (1-p) / n)
where p is the proportion and n is the sample size.
In this case, p = 0.7 (70% of the students live in the dormitories) and n = 75.
SE = sqrt(0.7 * (1-0.7) / 75) = 0.0529
Therefore, the standard error of the proportion is approximately 0.0529 and the best choice is C.
SE = sqrt(p * (1-p) / n)
where p is the proportion and n is the sample size.
In this case, p = 0.7 (70% of the students live in the dormitories) and n = 75.
SE = sqrt(0.7 * (1-0.7) / 75) = 0.0529
Therefore, the standard error of the proportion is approximately 0.0529 and the best choice is C.
Learning Objectives
- Comprehend the principle and significance of standard error within the context of statistical inference.
- Comprehend the impact of differing probabilities on the standard error associated with proportions.
Related questions
As a Rule of Thumb, the Sampling Distribution of the ...
Doubling the Size of the Sample Will ...
A Random Number Is Any Number Between Negative Infinity and ...
It Is Estimated That 780,000 Surgical Site Infections (SSIs)occur Each ...
It Is Estimated That 780,000 Surgical Site Infections (SSIs)occur Each ...