The Pearson correlation coefficient must be greater than 0.537 for the result to be statistically significant.
Given data is as follows:
Sample size, n=22
Level of significance, a=0.01
The test statistic for observed sample correlations coefficient is t= r√n-2 √1-2 t with n-2 degrees of freedom.
The critical value of t for a two-tailed test for 1% level of significane
for n-2-22-2-20 degrees of freedom is 2.85 In order to calculate the value of t significant at 1%, we should have
[tex]\frac{r\sqrt{n-2}}{\sqrt{1-r^2}} > t_{0.01}\\\\\implies\frac{r\sqrt{20}}{\sqrt{1-r^2}} > 2.85[/tex]
2022.852 = (1-µ³)
or (20+2.852)² >2.852
or 28.1225x2>8.1225
or 2r > 8.1225> 28.1225 = 0.28883
Hence r > 0.28883 = 0.537
Therefore the Pearson correlation coefficient must be greater than 0.537 for the result to be statistically significant at α = 0.01 .
Disclaimer: The complete question is :
How large must a Pearson correlation coefficient, calculated on a sample of 22 people, be to be statistically significant at the alpha = 0.01 .
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