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.
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