SOLUTION: 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 betwee

Question 197815: 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
Part 1 (10 points0: 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:
Using the r calculated, test the significance of the correlation coefficient using a = 0.01 and the claim k = 0. Design the test using the 7-steps hypothesis test.
Answer:
1. H0 : k = 0
Ha : k
2. a = 0.01
3. Find the test statistic t.
4. Find the critical t0
5. Define the rejection region.
6. State the statistical decision.
7. Application interpretation.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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
Part 1 (10 points0: 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:
---
Add the "Years" numbers and divide by 9 to get the following
Mean: 5.1111...
------------------------
Comment: the r value is 0.933675...
------------------------
Using the r calculated, test the significance of the correlation coefficient using a = 0.01 and the claim k = 0. Design the test using the 7-steps hypothesis test.
Answer:
1. H0 : k = 0
Ha : k is not 0
2. a = 0.01
3. Find the test statistic t.
t = 0.933675/sqrt[(1-0.933675^2)/(9-2)] = 6.8977
-----------------------------------
4. Find the critical t0
Critical values for a 2-tail test with alpha = 1% and df = 8 is t = 3.355
------------------------------------
5. Define the rejection region.
t-values that are less than -3.355 or greater than 3.355
---------------------------------------------
6. State the statistical decision.
Since the test statistic is in the reject interval, reject Ho.
------------------------------------------------
7. Application interpretation.
We reject the Ho claim that there is no linear correlation between
years of study and grades. The test results imply there is some
linear correlation between those factors.
======================================================
Cheers,
Stan H.

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