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
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 
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 for the slope of the regression line indicates the range of values within which the true slope is likely to fall with 99% confidence. Since the slope represents the average change in test score for every additional year spent studying Spanish, the interval (5.05, 16.76) suggests that, on average, the test score increases between 5.05 and 16.76 points for each additional year of Spanish study. Therefore, choice D is the best answer. Option A and B are not correct because the confidence interval is for the slope of the regression line, not for the mean test score. Option C and E are incorrect because they imply that the average test score decreases or the number of years of Spanish study increases, which is opposite to what the confidence interval suggests.

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