Chapter 3, Problem 4PT

To determine

To find:the truestatement from the given statement.

Answer to Problem 4PT

The correct answer is Statement 1

Explanation of Solution

Given:

  $Calculator=-1.2+0.865(pencil)$ r = 0.79

Calculation:

1. “If the student had used calculator as the explanatory variable, the correlation would remain the same”. This statement is true because correlation (r) makes no distinction between explanatory and response variables. It makes no difference which variable you call X and which you call Y in calculating the correlation.
2. “If the student had used calculator as the explanatory variable, the slope of the least squared lined would remain the same”. This statement is false because.

  $Slope=r\frac{{\sigma }_y}{{\sigma }_X}$

Value of slope would not remain same if we switch explanatory and response variable.

3. “The standard deviation of the number of correct answers on the paper − and −pencil quizzes was larger than the standard deviation on the calculator quizzes”. This is statement is false since,

  $Slope=r\frac{{\sigma }_{calculator}}{{\sigma }_{pencil}}$

  $0.865=0.79\times \frac{{\sigma }_{calculator}}{{\sigma }_{pencil}}$

  $\Rightarrow \frac{{\sigma }_{calculator}}{{\sigma }_{pencil}}=\frac{0.865}{0.79}$

1

If $\frac{{\sigma }_{calculator}}{{\sigma }_{pencil}}>1\Rightarrow {\sigma }_{calculator}>{\sigma }_{pencil}$

The standard deviation of the number of correct answers on the calculator quizzes was larger than the standard deviation on the paper −and −pencil quizzes”.

Conclusion:

Hence it is said that only statement 1 is true