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Comprehension:
Direction: Based on the following information, answer the questions.
For an experiment, a sample of 25 observations from normal distribution with mean 98.6 and s.d. 17.2 was selected. Answer the following questions:
What is the standard error of mean for a sample size n = 36?
  • a)
    2.86
  • b)
    3.123
  • c)
    4
  • d)
    0.478
Correct answer is option 'A'. Can you explain this answer?
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Comprehension:Direction: Based on the following information, answer th...
Concept:
The standard error of mean:

Calculation:
We have σ = 17.2
Sample size, n = 36
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Comprehension:Direction: Based on the following information, answer th...
Standard Error of Mean:
The standard error of the mean (SEM) is a measure of the precision of the sample mean as an estimate of the population mean. It indicates the average amount of variability or dispersion in the sample means across multiple samples.

Given Information:
- Sample size (n) = 25
- Mean (μ) = 98.6
- Standard deviation (σ) = 17.2

Formula:
The standard error of the mean can be calculated using the formula:

SEM = σ / √n

where σ is the standard deviation and n is the sample size.

Calculating Standard Error of Mean:
In this case, we are given a sample size of 25. However, we need to calculate the standard error of the mean for a sample size of 36.

Using the formula, we can calculate the standard error of the mean as follows:

SEM = 17.2 / √36
= 17.2 / 6
= 2.86

Answer:
Therefore, the standard error of the mean for a sample size of 36 is 2.86.

Summary:
- The standard error of the mean (SEM) is a measure of the precision of the sample mean as an estimate of the population mean.
- It is calculated using the formula SEM = σ / √n, where σ is the standard deviation and n is the sample size.
- In this case, the standard error of the mean for a sample size of 36 is 2.86.
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