# Correlation Coefficient & 7-step Hypothesis Test

In order for applicants to work for the state 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.

Applicant # 1 2 3 4 5 6 7 8 9

Years, x 4 5 5 6 4 7 3 8 4

Grades, y 62 69 76 83 74 91 59 94 73

Find the mean years for study for the 9 randomly selected applicants. Show the formula that you will use and then calculate the mean age.

Answer: Formula:

Mean:

Interpret the type of correlation by completing the table and calculating the correlation coefficient r rounded to the nearest three decimal places. Interim rounding should be four decimal places.

x y xy x2 y2

4 62

5 69

5 76

6 83

4 74

7 91

3 59

8 94

4 73

Use the last row of the table to show the column totals.

Interpret the type of correlation:

Using the r calculated, test the significance of the correlation coefficient using  = 0.01 and the claim  = 0. Design the test using the 7-steps hypothesis test.

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#### Solution Summary

The solution provides step by step method for the calculation of mean and test statistic for significance of correlation coefficient . Formula for the calculation and Interpretations of the results are also included.