A random sample of size n is to be drawn from a population with a mean = 500 and sd = 100. What sample size would be necessary to ensure a standard error of 25? Sample sizes are whole numbers.

Question

A random sample of size n is to be drawn from a population with a mean = 500 and sd = 100. What sample size would be necessary to ensure a standard error of 25? Sample sizes are whole numbers.

Answer 1

SEm = SD/√n

25 = 100/n

Solve for n.

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Answer 2

In a poll, 1,001 adults in a certain country were asked whether they favor or oppose the use of "federal tax dollars to fund medical research using stem cells obtained from human embryos." Based on the poll results, it is estimated that 47% of adults are in favor, with a margin of error of 4 percentage points. Use the given statistic and margin of error to identify the range of values (confidence interval) likely to contain the true value of the population parameter.

Answer 3

To determine the sample size necessary to ensure a standard error of 25, we can use the formula:

Standard Error (SE) = Standard Deviation (SD) / √Sample Size (n)

Given that the standard deviation (SD) is 100 and the desired standard error is 25, we can rearrange the formula to solve for the sample size (n):

25 = 100 / √n

First, square both sides of the equation to get rid of the square root:

25^2 = (100 / √n)^2

625 = 100^2 / n

Multiply both sides of the equation by n to isolate it:

625n = 100^2

n = 100^2 / 625

n ≈ 16

Therefore, a sample size of approximately 16 would ensure a standard error of 25. Since the sample size should be a whole number, we can round this up to the nearest whole number:

n = 17

Hence, a sample size of 17 would be necessary in this case to ensure a standard error of 25.

Answer 4

To determine the sample size necessary to ensure a standard error of 25, we need to use the formula for standard error:

Standard Error (SE) = Standard Deviation (SD) / √(Sample Size)

In this case, the standard deviation (SD) is given as 100, and the desired standard error (SE) is 25.

Substituting these values into the formula, we get:

25 = 100 / √(Sample Size)

To solve for the sample size, we can cross-multiply and square both sides of the equation:

25^2 * Sample Size = 100^2

625 * Sample Size = 10,000

Dividing both sides by 625:

Sample Size = 10,000 / 625 = 16

Thus, a sample size of 16 would be necessary to ensure a standard error of 25.