The following table lists the National Basketball Association’s leading scorers,

Question

The following table lists the National Basketball Association’s leading scorers, their average points per game (PPG), and their average minutes per game (MPG) for 2008. Use Table 2.

Calculate the sample correlation coefficient between PPG and MPG. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

Specify the competing hypotheses in order to determine whether the population correlation between PPG and MPG is positive.

H0: xy 0; HA: xy > 0

Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

At the 5% significance level, what is the conclusion to the test?

The following table lists the National Basketball Association’s leading scorers, their average points per game (PPG), and their average minutes per game (MPG) for 2008. Use Table 2.

TABLE 2 Student's Distrib Entles n prortde the odned for TABLE 2 IContinuedo that to a given ber of deg of food For A76 .328 0.10 575 /571 2.770 2.080 2.074 037 2024 2.020 2008 005 2.000 2449 2429 2402 2400 239 239) 2345 2334 4604 4032 3707 3499 3106 2098 285 2019 2750 0.00 2.744 2.700 2,724 2.674 2.062

Explanation / Answer

(a) correlation coefficeint=0.09 ( two decimal place)

using the ms-excel we generated follwoing information

corr(x,y)=cov(x,y)/sqrt(var(x)*var(y))=0.2568/sqrt(5.0756*1.6404)=0.0889

(b) H0: xy 0; HA: xy > 0

(c1)we use t-test for significance of correlation coefficient and

t=r*sqrt(n-2)/sqrt(1-r*r)=0.0889*sqrt(10-2)/sqrt(1-0.0889*0.0889)=0.2524 with n-2=10-2=8 df

(c2)p-value > 0.20

one tailed p-value=0.0435 ( using ms-excel command =TDIST(0.2524,8,1))

(d1) Do not reject H0; we cannot state PPG and MPG are positively correlated.

since p-value is more than alpha=0.05

(d2) yes, we expect positve correlation should be significant

PPG(x) MPG(y) 30.4 37.8 30.4 36.8 28.5 35.3 27.7 36.4 27.6 35.5 27.1 38.4 24.6 37.9 24.6 34.1 24.5 37.5 24.4 36.7 var 5.0756 1.6404 cov(x,y)= 0.2568 corr(x,y)= 0.088997

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