Question

For a random sample of size n = 25, the correlation is r = 0.31 for normal random variables X and Y. Answer the questions for the hypothesis test. Use a level of significance of a =0.08. Ho: p=0 H:P+0 a. The critical value is Z = b. The test statistic is Z= c. The p-value is d. The hypothesis (should, should not) be rejected.

Answer 1

Answer: Given data, n-25, 80.31. and a=0.08 a) As we are testing here whether there is a correlation between the two variables, and we are testing it from both sides, these fose this is a two-tailed test. For level of significance 0.08 and Degree of freedom of : 04=25-2-23. we have from a distribution tables: P(t23 <1832) -0.96 =>p[ +93 >1832)=0.04. - P(+972-1-832) + P(+2371-832) - 0.04*2 = 0.08. therefore 7 = +1832 ade the required critical values bede. by the restatistic is. ofn-2 0.31 * $23 = 1.56 -03? -82 fest statistic = 1.56 o As this is a two-tailed test for df = 23 we get the p-value from t- distribution table. P- 2P(+2371-56)=2* 0.0662 -0.1324 : The required p-value = 0.1324 o Aere the P-value > 0.08(d). The test is not significant here, and the null hypothesis should not be rejected here. thank you