Question

if standard deviation of a population is 20 and standard error of mean is 4,then the sample size will be what?​

Answer 1

$\huge\mathbb{\underline{Answer:-}}$

➢The standard error is also inversely proportional to the sample size; the larger the sample size, the smaller the standard error because the statistic will approach the actual value. The standard error is considered part of descriptive statistics. It represents the standard deviation of the mean within a dataset .

Answer 2

The Sample size of the given data will be 25.

Given,

S = 20

SEM = 4

To Find,

The sample size.

Solution,

Before solving the question, let's understand the concept,

A larger sample size will result in a smaller standard error because the statistic will approach the real value. In descriptive statistics, the standard error is considered. This is a measure of the standard deviation of a dataset's mean.

Formula,

SME = S/√N

SME = standard error of the mean.

S = standard deviation.

N = sample size.

Now, let's solve the question,

4 = 20/√N

√N = 20 /4

On dividing, we get,

√N = 5

On squaring both sides, we get

(√N)² = 5²

N = 25.

The Sample size of the given data will be 25.

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