91Ó°ÊÓ

Based on the following: Students, teachers, and administrators were asked which of three teacher characteristics (challenging, enthusiastic, strict) they considered most important for a successful classroom experience. Five hundred people in a high school community were surveyed with the following results: $$\begin{array}{|l|c|c|c|} \hline & \text { Challenging } & \text { Enthusiastic } & \text { Strict } \\ \hline \text { Student } & 50 & 150 & 50 \\ \hline \text { Teacher } & 125 & 50 & 25 \\ \hline \text { Administrator } & 15 & 10 & 25 \\ \hline\end{array}$$ What percentage of those surveyed were students? (A) \(10 \%\) (B) \(20 \%\) (C) \(30 \%\) (D) \(40 \%\) (E) \(50 \%\)

A rural college is considering constructing a windmill to generate electricity but is concerned over noise levels. A study is performed measuring noise levels (in decibels) at various distances (in feet) from the campus library, and a least squares regression line is calculated with a correlation of \(0.74 .\) Which of the following is a proper and most informative conclusion for an observation with a negative residual? (A) The measured noise level is 0.74 times the predicted noise level. (B) The predicted noise level is 0.74 times the measured noise level. (C) The measured noise level is greater than the predicted noise level. (D) The predicted noise level is greater than the measured noise level. (E) The slope of the regression line at that point must also be negative.

A study of department chairperson ratings and student ratings of the performance of high school statistics teachers reports a correlation of \(r=1.15\) between the two ratings. From this information we can conclude that (A) chairpersons and students tend to agree on who is a good teacher. (B) chairpersons and students tend to disagree on who is a good teacher. (C) there is little relationship between chairperson and student ratings of teachers. (D) there is strong association between chairperson and student ratings of teachers, but it would be incorrect to infer causation. (E) a mistake in arithmetic has been made.

Suppose the correlation is negative. Given two points from the scatterplot, which of the following is possible? I. The first point has a larger \(x\) -value and a smaller \(y\) -value than the second point. II. The first point has a larger \(x\) -value and a larger \(y\) -value than the second point. III. The first point has a smaller \(x\) -value and a larger \(y\) -value than the second point. (A) I only (B) II only (C) III only (D) I and III only (E) I, II, and III

Suppose the regression line for a set of data, \(\hat{y}=3 x+b\), passes through the point (2,5) . If \(\bar{x}\) and \(\bar{y}\) are the sample means of the \(x\) - and \(y\) -values, respectively, then \(\bar{y}=\) (A) \(\bar{x}\). (B) \(\bar{x}-2 .\) (C) \(\bar{x}+5\). (D) \(\mu_{\bar{x}}\). (E) \(3 \bar{x}-1\)

Which of the following statements about correlation \(r\) is true? (A) A correlation of o.2 means that \(20 \%\) of the points are highly correlated. (B) Perfect correlation, that is, when the points lie exactly on a straight line, results in \(r=0\). (C) Correlation is not affected by which variable is called \(x\) and which is called \(y\). (D) Correlation is not affected by extreme values. (E) A correlation of o.75 indicates a relationship that is 3 times as linear as one for which the correlation is only \(0.25 .\)

Which of the following statements about residuals from the least squares line are true? I. The mean of the residuals is always zero. II. The regression line for a residual plot is a horizontal line. III. A definite pattern in the residual plot is an indication that a nonlinear model will show a better fit to the data than the straight regression line. (A) I and II only (B) I and III only (C) II and III only (D) I, II, and III (E) None of the above gives the complete set of true responses.

Data are obtained for a group of college freshmen examining their SAT scores (Math + Evidence-Based Reading and Writing) from their senior year of high school and their GPAs during their first year of college. The resulting regression equation is $$ \widehat{\mathrm{GPA}}=0.55+0.00161 \text { (SAT score) } \quad \text { with } \quad r=0.632 $$ What percentage of the variation in GPAs can be accounted for by looking at the linear relationship between GPAs and SAT scores? (A) \(0.161 \%\) (B) \(16.1 \%\) (C) \(39.9 \%\) (D) \(63.2 \%\) (E) This value cannot be computed from the information given.

Suppose the correlation between two variables is \(r=0.23 .\) What will the new correlation be if 0.14 is added to all values of the \(x\) -variable, every value of the \(y\) -variable is doubled, and the two variables are interchanged? (A) 0.74 (B) 0.37 (C) 0.23 (D) -0.23 (E) -0.74

A company employs both men and women in its secretarial and executive positions. In reports filed with the government, the company shows that the percentage of female employees who receive raises is higher than the percentage of male employees who receive raises. A government investigator claims that the percentage of male secretaries who receive raises is higher than the percentage of female secretaries who receive raises and that the percentage of male executives who receive raises is higher than the percentage of female executives who receive raises. Is this possible? (A) No, either the company report is wrong or the investigator's claim is wrong. (B) No, if the company report is correct, either a greater percentage of female secretaries than of male secretaries receive raises or a greater percentage of female executives than of male executives receive raises. (C) No, if the investigator is correct, by summation of the corresponding numbers, the total percentage of male employees who receive raises would have to be greater than the total percentage of female employees who receive raises. (D) All of the above are true. (E) It is possible for both the company report to be true and the investigator's claim to be correct.