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

question 11

Multiple Choice

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 95% confidence interval for the mean score of all applicants who have
Studied Spanish for 4.6 years was determined to be (75.6, 87.7) .Give an interpretation of this
Interval. Dependent variable is: Score
$R$ squared $= 83.09$
$s = 5.65138$ with $10 - 2 = 8$ degrees of freedom
$\begin{array} { l l l l l } \text { Variable } & \text { Coefficient } & \text { s.e. of Coeff } & \text { t-ratio } & \text { prob } \\ \text { Constant } & 31.53333 & 6.360418 & 4.957745 & 0.00111 \\ \text { Number of years } & 10.90476 & 1.744054 & 6.252538 & 0.000245 \end{array}$

• A) Based on this regression, we are \(95 \%\) confident that a randomly selected applicant who has studied Spanish for \(4.6\) years will score between \(75.6\) and \(87.7\) points on the proficiency test.
• B) Based on this regression, we are \(95 \%\) confident that applicants will score between \(75.6\) and \(87.7\) points higher on the proficiency test for each additional year spent studying Spanish.
• C) Based on this regression, we are \(95 \%\) confident that all applicants who have studied Spanish for \(4.6\) years will average between \(75.6\) and \(87.7\) points on the proficiency test.
• D) Based on this regression, we are \(95 \%\) confident an applicant who has studied Spanish for \(4.6\) years will score between \(75.6\) and \(87.7\) points on the proficiency test.
• E) Based on this regression, \(95 \%\) of all random samples will have an average score between \(75.6\) and \(87.7\) points on the proficiency test.

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Definitions:

Normal Good

A good for which demand increases when income increases, and falls when income decreases but price remains constant, showing a direct relationship between income and demand.

Income Elasticity

A measure of how much the demand for a good or service changes in response to a change in consumers' income levels.

Normal Good

A good for which demand increases as consumer income rises, and decreases as consumer income falls.

Inferior Good

A type of good for which demand decreases as the income of the consumer increases, as opposed to a normal good where demand increases with income.