In order for applicants to work for the foreign-service department, they must take a test in the language of the country where they plan to work. The data below shows the relationship between the number of years that applicants have studied a particular language and the grades they received on the proficiency exam. Number of years, x 4 3 4 5 3 6 2 7 3 Grades on the proficiency exam, y 62 66 76 84 73 90 61 96 72 (a) Find the correlation coefficient expressed to 3 decimal places: r= (b) Between the number of years that the applicant has studied the language and the grade on the proficiency exam there is a weak, positive, linear association a strong, positive, linear association no association a strong, negative, linear association (c) Find the equation of the least-squares regression line, y^=bx+a, for the given data. y= x+ Express a and b to 3 significant digits.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
In order for applicants to work for the foreign-service department, they must take a test in the language of the country where they plan to work. The data below shows the relationship between the number of years that applicants have studied a particular language and the grades they received on the proficiency exam.
| Number of years, x | 4 | 3 | 4 | 5 | 3 | 6 | 2 | 7 | 3 |
| Grades on the proficiency exam, y | 62 | 66 | 76 | 84 | 73 | 90 | 61 | 96 | 72 |
(a) Find the
r=
(b) Between the number of years that the applicant has studied the language and the grade on the proficiency exam there is
|
a weak, positive, linear association |
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a strong, positive, linear association |
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no association |
||
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a strong, negative, linear association |
(c) Find the equation of the least-squares regression line, y^=bx+a, for the given data.
y= x+
Express a and b to 3 significant digits.
(d) Predict the grade an applicant will receive on the profficiency exam if the applicant studied the particular language for 8 years.
(Express answer to 3 significant digits)
(e) Interpret the value of the slope of the least-squares regression line in the context of this problem.
The model predicts that for each additional one year spent practicing, the grade on the proficiency exam
|
decreases |
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|
increases |
by points on average. (Express answer to 3 significant digits)
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