Answer to Question #264560 in Statistics and Probability for Nisham

Question

Tell what will happen to each standard error of the mean when the sample size:

1. increased from 50 to 200? Explain

2. decreased from 250 to 225? Explain

3. increased from 200 to 400? Explain

4. increased from 40 to 50? Explain

5. decreased from 600 to 40? Explain

Answer 1

1. If sample size is increased from 50 to 200 then standard error of the mean will decrease. It is because an inverse relationship exists between the standard error of the mean and the sample size. A larger sample size leads to smaller value of the standard deviation.

2. If sample size is decreased from 250 to 225 then the value of standard error will increase. In case of decrease in sample size, smaller data values are clustered to the mean that leads to increase in the standard error of the mean.

3. If sample size is increased from 200 to 400 then the standard error of the sampling distribution of the mean will be declined. Sample means cluster more closely around the population mean in case of large sample size that has potential to smaller the spread.

4. If sample size is increased from 40 to 50 then standard error will decrease due to inverse relationship between two variables.

5. In case of decrease in sample size from 600 to 40, the standard error of the mean will be declined. Standard error equals the standard deviation divided by the square root of the sample size, so increase or decrease in sample size leads to fall or rise in the standard error.