A sample of 28 observations provides the following statistics: Use Table 2. sx =

Question

A sample of 28 observations provides the following statistics: Use Table 2. sx = 17, sy = 25, and sxy = 118.96 a-1. Calculate the sample correlation coefficient rxy. (Round your answer to 2 decimal places.) Sample correlation coefficient a-2. Interpret the sample correlation coefficient rxy. The correlation coefficient indicates a positive linear relationship. The correlation coefficient indicates a negative linear relationship. The correlation coefficient indicates no linear relationship. b. Specify the hypotheses to determine whether the population correlation coefficient is positive. H0: xy = 0; HA: xy 0 H0: xy 0; HA: xy < 0 H0: xy 0; HA: xy > 0 c-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic c-2. Approximate the p-value. 0.05 < p-value < 0.100 0.010 < p-value < 0.025 0.100 < p-value < 0.200 p-value > 0.200 d. At the 5% significance level, what is the conclusion to the test? Reject H0; we can state the population correlation is positive. Reject H0; we cannot state the population correlation is positive. Do not reject H0; we can state the population correlation is positive. Do not reject H0; we cannot state the population correlation is positive.

Explanation / Answer

a1)here rxy=Sxy/(Sx*Sy) =0.2799

a-2)The correlation coefficient indicates a positive linear relationship

b)  H0: xy 0; HA: xy > 0

c1) here n=28

hence test stat t=r((n-2)/(1-r2))1/2 =1.486

c-2)p value for above test stat =0.0746

0.05 < p-value < 0.100

d) Do not reject H0; we cannot state the population correlation is positive.

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