Question
Asked Jan 16, 2020
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Oscars Listed below are ages of Oscar winners matched by the years in which the awards were won (from Data Set 14 “Oscar Winner Age” in Appendix B). Is there sufficient evidence to conclude that there is a linear correlation between the ages of Best Actresses and Best Actors? Should we expect that there would be a correlation?

Old
16
27
17
33
28
24
18
22
20
29
21
New
15
24
15
29
25
22
16
20
18
26
19
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Old 16 27 17 33 28 24 18 22 20 29 21 New 15 24 15 29 25 22 16 20 18 26 19

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Expert Answer

Step 1

The t-test for correlation coefficient will use to conclude if there is a linear correlation between the ages of Best Actresses and Best Actors.

The hypothesis can be written as:

H0: There is no linear correlation between the ages of best Actresses and Best Actors.

Ha: There is a linear correlation between the ages of best Actresses and Best Actors.

Consider x represents the ages of Best Actresses and y represents the ages of Best Actors.

The total number of observations (n) are 11.

The correlation between x and y can be obtained as:

Statistics homework question answer, step 1, image 1
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Step 2

The absolute value of t statistic can be obtained as:

Statistics homework question answer, step 2, image 1
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Step 3

The degree of freedom for this test is (n-2) so, the degree of freedom is (11-2)=9

Let the level of significance is α=0.05, the crit...

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