Question

1. (a) Using R and R Commander, run the Correlation test between the variables attpublicschools and attteachingprof. Copy appropriate output and paste it below this question. Is the correlation significant at 5% alpha level?                                                                                   [6 Points]

I have done the correlation test. (see below for data) How do I know if the correlation significant at 5% alpha level? Is 5% alpha the same as 95% confidence interval?

Pearson's product-moment correlation

data: attpublicschools and attteachingprof

t = 3.724, df = 22, p-value = 0.001179

alternative hypothesis: true correlation is not equal to 0

95 percent confidence interval:

0.2915420 0.8196169

sample estimates:

      cor

0.6218095

Answer 1

we have given output of the correlation test : t statistics , p value .

correlation test :

To test :

Ho : ρ = 0 VS H1 : ρ ≠ 0

( it is two sided test )

where ρ population correlation coefficient .

Test statistics : t =

t = 3.724,

df = 22 ( degree of freedom )

p-value = 0.001179

α = 95 % ie 0.05 ( level of significance)

Decision : We reject Ho if p value is less than α value using p value approach here p value is less than α value we reject Ho at given level of significance

Conclusion : There is sufficient evidence to conclude that population correlation is different than zero .

we can say it is significant at given level of significance .

### 95 percent confidence interval:

[ 0.2915420 , 0.8196169 ]

conclusion from the confidence interval : result is significant if interval does not include null value

here confidence interval is free from null value we can say that it is significant .

### here result is same from testing of hypothesis and confidence interval .