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Applicants for a particular job that involves extensive travel in Spanish speaking countries, must take a proficiency test in Spanish.

Applicants for a particular job that involves extensive travel in Spanish speaking countries, must take a proficiency test in Spanish.  The sample data below was obtained in a study of the relationship between the numbers of years applicants have studies Spanish and their score on the test.
# of Years (χ)     3 4 4 2 5 3 4 5 3 2
Score   57 78 72 58 89 63 73 84 75 48
Partial Minitab output is provided below.
Mintab----Regression Analysis
The regression equation is score = 31.5 + 10.9*years
S = 5.651 R -SQ = 83.0% R-Sq (adj) = 80.9%
Analysis of Variance
Source DF      SS MS     F
P
Regression 1 1248.6 1248.6 39.09
0.000
Residual Error 8 255.5 31.9
Total 9 1504.1
a. What is the correlation coefficient, r?
b. At the 5% level of significance, do the data provide sufficient evidence to conclude that the slope of the population regression line is not zero and hence that the number of years of study is useful as a predictor of score on the test? Explain.
c. do the data provide sufficient evidence to conclude that the number of years of study and test score are linearly positively correlated: Use α = 0.01.

χ) 3 4 4 2 5 3 4 5 3 2
Score 57 78 72 58 89 63 73 84 75 48
Partial Minitab output is provided below.
Mintab----Regression Analysis
The regression equation is score = 31.5 + 10.9*years
S = 5.651 R –SQ = 83.0% R-Sq (adj) = 80.9%
Analysis of Variance
Source DF SS MS F
P
Regression 1 1248.6 1248.6 39.09
0.000
Residual Error 8 255.5 31.9
Total 9 1504.1
a. What is the correlation coefficient, r?
і
†
в
д
ж
°
±
do the data provide sufficient evidence to conclude that the number of
years of study and test score are linearly positively correlated: Use α
= 0.01.

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