The standard error of the sample mean is given by the formula:

SE = σ/√n

where:
SE is the standard error,
σ is the standard deviation of the population, and
n is the size of the sample.

In this case, we know that the variance (σ^2) is 25, so the standard deviation (σ) is the square root of the variance, which is 5. We want the standard error (SE) to be 1.5.

Substituting these values into the formula, we get:

1.5 = 5/√n

To solve for n, we first square both sides of the equation to get rid of the square root:

(1.5)^2 = (5/√n)^2
2.25 = 25/n

Then, we multiply both sides by n and divide by 2.25 to solve for n:

n = 25/2.25
n = 11.11

Since the sample size must be a whole number, we round up to the nearest whole number, which is 12.

So, the sample size must be 12 (option e) to achieve a standard error of 1.5.

Question

The standard error of the sample mean is given by the formula:

SE = σ/√n

where:
SE is the standard error,
σ is the standard deviation of the population, and
n is the size of the sample.

In this case, we know that the variance (σ^2) is 25, so the standard deviation (σ) is the square root of the variance, which is 5. We want the standard error (SE) to be 1.5.

Substituting these values into the formula, we get:

1.5 = 5/√n

To solve for n, we first square both sides of the equation to get rid of the square root:

(1.5)^2 = (5/√n)^2
2.25 = 25/n

Then, we multiply both sides by n and divide by 2.25 to solve for n:

n = 25/2.25
n = 11.11

Since the sample size must be a whole number, we round up to the nearest whole number, which is 12.

So, the sample size must be 12 (option e) to achieve a standard error of 1.5.

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