Write the word or phrase that best completes each statement or answers the question.
-Scores on a test are normally distributed with a mean of 71 and a standard deviation of 11. For samples of size 35, which of the two variables below has more variation? Why? What is the distribution of each of the variables?
(a) $\frac { \bar { x } - 71 } { 11 / \sqrt { 35 } }$

(b) $\frac { \bar { x } - 71 } { s / \sqrt { 35 } }$

Question

Write the word or phrase that best completes each statement or answers the question.
-Scores on a test are normally distributed with a mean of 71 and a standard deviation of 11. For samples of size 35, which of the two variables below has more variation? Why? What is the distribution of each of the variables? 
 (a) $\frac { \bar { x } - 71 } { 11 / \sqrt { 35 } }$

(b) $\frac { \bar { x } - 71 } { s / \sqrt { 35 } }$

Quizplus · Accepted Answer

The Answer is The variable in (b)has more variation since its variation is due to the variation of both the sample means and the sample standard deviations. The variation of the variable in (a)is due solely to the variation of the sample means. The variable in (a) has a standard normal distribution while the variable in (b)has a t-distribution with 34 degrees of freedom.

Write the Word or Phrase That Best Completes Each Statement xˉ−7111/35\frac { \bar { x } - 71 } { 11 / \sqrt { 35 } }11/35​xˉ−71​

Write the Word or Phrase That Best Completes Each Statement $\frac { \bar { x } - 71 } { 11 / \sqrt { 35 } }$