Question

Suppose that in a random sample of size 200, standard deviation of the sampling distribution of the sample mean 0.08. researcher wanted to reduce the standard deviation to 0.04. what sample size would be required?

Answer 1

To reduce the standard deviation of the sampling distribution from 0.08 to 0.04, the researcher needs to increase the sample size by a factor of 4, resulting in a new sample size of 800.

Step-by-step explanation:

The subject of the question involves statistics, specifically the sampling distribution of the sample mean. The standard deviation of the sampling distribution is related to the sample size through the formula σx = σ / √n, where σx is the standard deviation of the sampling distribution of the sample mean, σ is the population standard deviation, and n is the sample size. To cut the standard deviation of the sampling distribution in half, from 0.08 to 0.04, we must increase the sample size by a factor of 4 (since σx is inversely proportional to the square root of n).

To find the required sample size, if the current sample size of 200 gives a standard deviation of 0.08, when we want to reduce that to 0.04, we perform the following calculation:

• (0.08 / 0.04)² = (√n / √200)²
• 4 = n / 200
• n = 4 × 200
• n = 800

Therefore, the researcher would need a sample size of 800 to reduce the standard deviation of the sampling distribution to 0.04.

Answer 2

400

Step-by-step explanation:

The computation of the sample size needed is shown below:

Since at the sample size of 200 there is a standard deviation of 0.08

But when the standard deviation is 0.04 so the sample size is 400

As sample standard deviation would be inversely proportional to the square root of the sample size