Alice Ben Connie and Dwayne have each taken a random sample

Alice, Ben, Connie and Dwayne have each taken a random sample of students from their school to estimate the variability in amount spent on movie tickets this summer. Alice asked 10 people, Ben 30, Connie 50, and Dwayne 70. Whose sample standard deviation probably differs most from the population parameter? Give a reason for your answer.

Solution

Alice, Ben, Connie and Dwayne have each taken a random sample of students from their school to estimate the variability in amount spent on movie tickets this summer. Alice asked 10 people, Ben 30, Connie 50, and Dwayne 70. Whose sample standard deviation probably differs most from the population parameter? Give a reason for your answer.

Alice’s sample standard deviation probably differs most from the population parameter.

Sample size of Alice’s is 10 which is smaller than the other three.

Standard deviation is the square root of the summation of each individual element\'s difference from the average squared divided by the number of elements in the sample.

Generally standard deviation decreases when sample size increases.

When sample size increases, the sample standard deviation approaches population standard deviation.

So Alice’s sample standard deviation probably larger than others and differs most from the population parameter.