Applicants for a particular job,which involves extensive travel in Spanish-speaking countries,must take a proficiency test in Spanish.The sample data were obtained in a study of the relationship between the numbers of years applicants have studied Spanish and their score on the test.A 99% confidence interval for the slope of the regression line was determined to be (5.05,16.76).Give an interpretation of this interval. Dependent variable is: Score
R-squared = 83.0%
S = 5.65138 with 10 - 2 = 8 degrees of freedom $$\begin{array} { l l l l l }
\text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-ratio } & \text { P-value } \
\text { Constant } & 31.53333 & 6.360418 & 4.957745 & 0.00111 \
\text { Number of years } & 10.90476 & 1.744054 & 6.252538 & 0.000245
\end{array}$$
A)Based on these data,we are 99% confident that the mean test score is between 5.05 and 16.76 points.
B)Based on these data,we are 99% confident that a randomly selected applicant will score between 5.05 and 16.76 points on the test.
C)Based on these data,we are 99% confident that the average test score decreases between 5.05 and 16.76 points for every additional year spent studying Spanish.
D)Based on these data,we are 99% confident that the average test score increases between 5.05 and 16.76 points for every additional year spent studying Spanish.
E)Based on these data,we are 99% confident that the number of years spent studying Spanish increases between 5.05 and 16.76 years for every additional point earned on the test.

Question

Applicants for a particular job,which involves extensive travel in Spanish-speaking countries,must take a proficiency test in Spanish.The sample data were obtained in a study of the relationship between the numbers of years applicants have studied Spanish and their score on the test.A 99% confidence interval for the slope of the regression line was determined to be (5.05,16.76).Give an interpretation of this interval. Dependent variable is: Score
R-squared = 83.0%
S = 5.65138 with 10 - 2 = 8 degrees of freedom $$\begin{array} { l l l l l } 
\text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-ratio } & \text { P-value } \
\text { Constant } & 31.53333 & 6.360418 & 4.957745 & 0.00111 \
\text { Number of years } & 10.90476 & 1.744054 & 6.252538 & 0.000245
\end{array}$$
A)Based on these data,we are 99% confident that the mean test score is between 5.05 and 16.76 points.
B)Based on these data,we are 99% confident that a randomly selected applicant will score between 5.05 and 16.76 points on the test.
C)Based on these data,we are 99% confident that the average test score decreases between 5.05 and 16.76 points for every additional year spent studying Spanish.
D)Based on these data,we are 99% confident that the average test score increases between 5.05 and 16.76 points for every additional year spent studying Spanish.
E)Based on these data,we are 99% confident that the number of years spent studying Spanish increases between 5.05 and 16.76 years for every additional point earned on the test.

Quizplus · Accepted Answer

The confidence interval given is for the slope of the regression line, which represents the average change in the test score for every additional year spent studying Spanish. The interval (5.05, 16.76) indicates that we are 99% confident that on average, the test score increases between 5.05 and 16.76 points for every additional year spent studying Spanish. Therefore, option D is the best choice. Option A and B are incorrect because they refer to the mean test score, which is not the focus of the interval. Option C and E are also incorrect because they imply a decrease or increase in the number of years spent studying Spanish, which is not the interpretation of the interval.

Applicants for a Particular Job,which Involves Extensive Travel in Spanish-Speaking