Question

Suppose an x distribution has mean μ = 4. Consider two corresponding x distributions, the first based on samples of size n = 49 and the second based on samples of size n = 81.

(a) What is the value of the mean of each of the two x distributions?

For n = 49, μ x =

For n = 81, μ x =

(b) For which x distribution is P( x > 5) smaller? Explain your answer.

The distribution with n = 49 because the standard deviation will be smaller.

The distribution with n = 81 because the standard deviation will be smaller.

The distribution with n = 49 because the standard deviation will be larger.

The distribution with n = 81 because the standard deviation will be larger.

(c) For which x distribution is P(3 < x < 5) greater? Explain your answer.

The distribution with n = 49 because the standard deviation will be smaller.

The distribution with n = 49 because the standard deviation will be larger.

The distribution with n = 81 because the standard deviation will be larger.

The distribution with n = 81 because the standard deviation will be smaller.

Answer 1

a)

We know that, if the sample size changes, the mean of the distribution does not change. Therefore, mean is same for both the sample.

For n = 49, mean = 4

For n = 81, mean = 4

b) we know, as sample size increases, spread of the data is decreases. That is, standard deviation is decreases. Therefore, P(X > 5) is decreases with increase in sample size because increase in sample size causes the standard deviation to be decrease.

The distribution with n = 81 because the standard deviation will be smaller.

c) As sample size increases, more observations are dense around mean because the standard deviation decreases.

The probability P(3 < X < 5) is greater for a sample with larger sample size because larger sample size causes decrease in standard deviation.

The distribution with n = 81 because the standard deviation will be smaller