Question

Consider two x distributions corresponding to the same x distribution. The first x distribution is based on samples of size n = 100 and the second is based on samples of size n = 225. Which x distribution has the smaller standard error? The distribution with n = 100 will have a smaller standard error. The distribution with n = 225 will have a smaller standard error. Explain your answer. Since σx = σ2/√n, dividing by the square root of 100 will result in a small standard error regardless of the value of σ2. Since σx = σ/n, dividing by 100 will result in a small standard error regardless of the value of σ. Since σx = σ/n, dividing by 225 will result in a small standard error regardless of the value of σ. Since σx = σ/√n, dividing by the square root of 100 will result in a small standard error regardless of the value of σ. Since σx = σ/√n, dividing by the square root of 225 will result in a small standard error regardless of the value of σ. Since σx = σ2/√n, dividing by the square root of 225 will result in a small standard error regardless of the value of σ2.

Answer 1

Answer:

The distribution with n = 225 will give a smaller standard error.

Since sigma x = sigma/√n, dividing by the square root of 225 will result in a small standard error regardless of the value of sigma.

Step-by-step explanation:

Standard error is given by standard deviation (sigma) divided by square root of sample size (√n).

The distribution with n = 225 would give a smaller standard error because the square root of 225 is 15. The inverse of 15 multiplied by sigma is approximately 0.07sigma which is smaller compared to the distribution n = 100. Square of 100 is 10, inverse of 10 multiplied by sigma is 0.1sigma.

0.07sigma is smaller than 0.1sigma