Question

The distribution of the commute times for the employees at a large company has mean 22.4 minutes and standard deviation 6.8 minutes. A random sample of n employees will be selected and their commute times will be recorded. What is true about the sampling distribution of the sample mean as n increases from 2 to 10 ? The mean increases, and the variance increases. A The mean increases, and the variance decreases.

B The mean does not change, and the variance does not change.

C The mean does not change, and the variance increases.

D The mean does not change, and the variance decreases.

The distribution of the number of siblings for students at a large high school is skewed to the right with mean 1.8 siblings and standard deviation 0.7 sibling. A random sample of 100 students from the high school will be selected, and the mean number of siblings in the sample will be calculated. Which of the following describes the sampling distribution of the sample mean for samples of size 100 ? Skewed to the right with standard deviation 0.7 sibling

A Skewed to the right with standard deviation less than 0.7 sibling

B Skewed to the right with standard deviation greater than 0.7 sibling

C Approximately normal with standard deviation 0.7 sibling

D Approximately normal with standard deviation less than 0.7 sibling

The distribution of height for a certain population of women is approximately normal with mean 65 inches and standard deviation 3.5 inches. Consider two different random samples taken from the population, one of size 5 and one of size 85. Which of the following is true about the sampling distributions of the sample mean for the two sample sizes? Both distributions are approximately normal with mean 65 and standard deviation 3.5.

A Both distributions are approximately normal. The mean and standard deviation for size 5 are both less than the mean and standard deviation for size 85.

B Both distributions are approximately normal with the same mean. The standard deviation for size 5 is greater than that for size 85.

C Only the distribution for size 85 is approximately normal. Both distributions have mean 65 and standard deviation 3.5.

D Only the distribution for size 85 is approximately normal. The mean and standard deviation for size 5 are both less than the mean and standard deviation for size 85.

Answer 1

Summary :-. Standard deviation ( standard error) decrease with increase of sample size . But mean will remain same as of population mean . No matter how small or big is sample size .

Now let's solve the question

1. As sample size increases from 2 to 10 the standard deviation will decrease and mean will remain same .

So correct option is option (D) .. mean does not change and standard deviation decrease.

2 again we took sample from population so mean will be same but standard deviation will increase .

So skewed to the right and standard deviation will be greater than 0.7 siblings. Option B

3. Now sample size 5 is less than sample size 85 so it will have greater standard deviation but same mean as of 85 .

So option B) is correct