Question

4. The annual per capita consumption of sugar by people in the US is a right skewed distributed with a mean of 150 pounds a standard deviation of 18.5 pounds. Random samples of size 65 are drawn from this population, and the mean of each sample is determined. (3 pts) a. Using Central Limit Theorem, what would the mean, standard deviation, and shape of the sampling distribution be? b. Now assume that random samples of size 110 are drawn instead. What would the mean, standard deviation and shape of the sampling distribution be? Which measures changed and how would they change?

Answer 1

Here we have : = 150, = 18.5

a. n = 65 , According to central limit theorem, as sample size increases sampling distribution of sample mean tends to normal distribution. Hence we get :

Mean =

Standard deviation =

Shape of distribution is symmetric, bell shaped.

b. Now n= 110

Mean =

Standard deviation =

Shape of distribution is symmetric, bell shaped.

Hence we can see that standard deviation is affected by changing of sample size. As sample size increases error decreases that is standard deviation is decreased.