The accompanying data on x = UV transparency index and y = maximum prevalence of infection was read from a graph in an article.

x	1.2	1.4	1.5	2.0	2.1	2.7	2.7	2.7	2.8	2.9	3.0	3.5	3.8	3.8	4.5	5.1	5.7
y	15	3	31	1	13	0	8	15	2	1	7	35	25	10	35	58	56

Summary quantities include

S_xx = 25.6506,

S_yy = 5546.2353,

and

S_xy = 265.1882.

(a)Calculate the value of the sample correlation coefficient. (Round your answer to three decimal places.)Interpret the value of the sample correlation coefficient.This indicates a weak, positive association between UV transparency index and maximum prevalence of infection.This indicates a moderate, negative association between UV transparency index and maximum prevalence of infection. This indicates a weak, negative association between UV transparency index and maximum prevalence of infection.This indicates a moderate, positive association between UV transparency index and maximum prevalence of infection.(b)If you decided to fit the simple linear regression model to this data, what proportion of observed variation in maximum prevalence could be explained by the model relationship? (Round your answer to three decimal places.)(c)If you decided to regress UV transparency index on maximum prevalence (i.e., interchange the roles of x and y), what proportion of observed variation could be attributed to the model relationship? (Round your answer to three decimal places.)(d)Carry out a test of

H₀: = 0.5

versus

H_a: > 0.5

using a significance level of 0.05. [Note: The article reported the P-value for testing

H₀: = 0

versus

H₀: 0.]

(Round your test statistic to two decimal places and your P-value to four decimal places.)z=P-value=State the conclusion in the problem context.Fail to reject H₀. We do not have sufficient evidence to conclude that the population correlation coefficient for these two variables exceeds 0.5.Reject H₀. We have sufficient evidence to conclude that the population correlation coefficient for these two variables exceeds 0.5. Reject H₀. We do not have sufficient evidence to conclude that the population correlation coefficient for these two variables exceeds 0.5.Fail to reject H₀. We have sufficient evidence to conclude that the population correlation coefficient for these two variables exceeds 0.5.