Suppose you are going to roll a six-sided die 60 times and record ,the proportion of times that an even number (2,4,or 6)is showing.Suppose you decide to roll the die 200 times instead of 60 times.How will this affect the center and spread of the sampling distribution of ?
A)Both the center and the spread will remain the same.
B)The center will remain the same,but the spread will increase.
C)The center will remain the same,but the spread will decrease.
D)Both the center and the spread will decrease.

Question

Suppose you are going to roll a six-sided die 60 times and record  ,the proportion of times that an even number (2,4,or 6)is showing.Suppose you decide to roll the die 200 times instead of 60 times.How will this affect the center and spread of the sampling distribution of  ?
A)Both the center and the spread will remain the same. 
B)The center will remain the same,but the spread will increase. 
C)The center will remain the same,but the spread will decrease. 
D)Both the center and the spread will decrease.

Quizplus · Accepted Answer

As the sample size (number of rolls) increases, the standard deviation of the sampling distribution decreases. This means that the spread of the sampling distribution will decrease. However, the center of the sampling distribution (the proportion of times an even number is showing) will remain the same because it is based on the probability of rolling an even number, which does not change regardless of the number of rolls. Therefore, the best answer is C, the center will remain the same but the spread will decrease.

Suppose You Are Going to Roll a Six-Sided Die 60