Question

Test for evidence of a linear association using the sample correlation r=0.68 and the sample size n=10.

State the null and alternative hypotheses.

  

  

Find the test statistic.

Round your answer to two decimal places.

t= Enter your answer; t


Find the p-value.

Round your answer to three decimal places.

The p-value is Enter your answer; p-value .


What is the conclusion, using a 5% significance level?

Choose the answer from the menu; What is the conclusion, using a 5% significance level?                                                                      Do not rejectReject H0.


Is the correlation significant?

Choose the answer from the menu; Is the correlation significant?                                                                      YesNo

Answer 1

State the null and alternative hypotheses.

Null hypothesis: H₀: The correlation coefficient is not statistically significant.

Alternative hypothesis: H_a: The correlation coefficient is statistically significant.

The test statistic value is given as below:

t = r*sqrt(n – 2)/sqrt(1 – r^2)

t = 0.68*sqrt(10 - 2)/sqrt(1 - 0.68^2)

t = 2.623157

Test statistic = 2.62

df = n - 2 = 10 - 2 = 8

P-value = 0.030501

(by using t-table)

P-value < α = 0.05

So, we reject the null hypothesis

Is the correlation significant?

The correlation coefficient is statistically significant.