Question

Question 1 20 pts Use the paired data below to test the claim that there is a correlation between x and y, using a=0.05. Round your answer to 3 decimal places. X 10 12 15 21 27 45 27 113 52 65 90 111 p-value=0.000, evidence not support claim p-value=0.000, evidence support claim p.value-5.1300, evidence not support claim p-value=0.999, evidence not support claim D-value-5.130, evidence support claim

Answer 1

Let p denotes the true correlation coefficient between the two variables. Hypotheses : To test null hypothesis H. :p =0 against alternative hypothesis H :P +0 Letr denotes the sample correlation coefficient between the two variables and n denotes the sample size. Here, r= 0.9994, n = 6 The test statistic can be written as: run - 2 t= r2 which under H, follows a t distribution with n -2 df. Decision rule / Rejection region : We reject Ho at 0.05 level of significance if P-value < 0.050 or if tobs | > to.025,0–2 = 2.776445 0.3- density 0.1- 0.0 - Now, Value of test statistic: The value of the test statistic t STAT = 58.463534 58.464 associated degrees of freedom = 4 The critical value == 2.776445 +2.776 P-value = P(|tn-21 > ESTAT) = 2 * P(t4 > 58.463534) = 2(1 – 1.000000) = 0.000001 Conclusion : Since p-value < 0.05 and tobs | > tcritical = 2.776, so we reject H, at 0.05 level of significance Hence, we can conclude that there is a significant linear correlation between two variables

ans-> ii) p-value - 0.000, evidence support claim.