Question
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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?

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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:

Step 2

The absolute value of t statistic can be obtained as:

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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