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# Correlation Coefficient & 7-step Hypothesis Test

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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.

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 &#61537; = 0.01 and the claim &#61547; = 0. Design the test using the 7-steps hypothesis test.