Question

Help A data set includes weights of garbage discarded in one week from 62 Stront households. The paired weight of paper and glass were used to obtain the results shown to the right is there suchen evidence to support the claim that there is a linear correlation between weights of discarded paper and glass? Use a significance level of 005 Click here to view a table of critical values for the correlation coefficient Correlation matrb Variables Paper Glass Paper 10.1511 Glass 0.1511 1 tents Determine the null and alternative hypotheses HO HP (Typengers or decimals. Do not round)
pleAse include test statistic and critical values and conclusion

Answer 1

Let p denotes the true correlation coefficient between the two variables. Hypotheses : To test null hypothesis Ho :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, p= 0.1511, n = 62 The test statistic can be written as: t= run - 2 V1 1 - p2 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 | > t0.025,n–2 = 2.000298 0.4- 0.3- density 0.2- 0.1- -6 6 0.0- 3 Now, Value of test statistic: The value of the test statistic t STAT = 1.184010 1.184 associated degrees of freedom = 60 The critical value =+ 2.000298 +2.000 P-value - P(|tn-2/ > tsTAT) = 2 * P(+60 > 1.184010) = 2(1 – 0.879461) = 0.241079 Conclusion : Since p-value > 0.05 and tobstcritical = 2.000298, so We fail to reject Ho at 0.05 level of significance Hence, we can conclude that there is not a significant linear correlation between two variables.