a sample of 28 observations provides the following statistics. sx=17 sy=25 and s

ID: 3051779 • Letter: A

Question

a sample of 28 observations provides the following statistics.

sx=17 sy=25 and sxy=118.96

a-1. calculate the sample correlation coeffecient Txy

a.2 Interpret the sample correlation coeffecient Txy

b. specify the hypotheses to determine whether the population correlation coeffecient is possible

c-1 calculate the value of the test statistic( round intermediate calc. to at least 4 decimals places and final answer 2 decimal places)

c-2 Approxiimate the p value

d. at the 5% signifigance level what is the conclusion to the test?

Solution:

Given information
sx=17 sy=25 and sxy=118.96
a-1) The sample correlation co-efficient Txy = Sxy / (Sx * Sy) = 118.96 / (17* 25) = 0.2799. (Ans).

a-2) The correlation co-efficient indicates a positive linear relationship. (Ans).

b) Thecorrect choice of hypothesis is H0: XY 0 against. XY > 0.

c-1) The value of the test-statistic, t = r n-2/1-r^2 , where, r = 0.2799, n = 28.

= 1.4866. (Ans).

c-2) p-value = P(t > 1.4866) , where t ~ T-distribution with (n-2) i.e. 26 d.f.

= 0.0746.
Thus 0.05 < p-value < 0.100

d) Since p-value > 0.05, we fail to reject H0 and we can not state population correlation is positive.

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