Homework SourseAn NBA coach would like to have an equal defense to keep the
An NBA coach would like to have an equal defense to keep their opponents from attacking one side. He wants to find out if his two starting forwards are equal in their defensive abilities. Over the last third of the season he keeps record of the scores per game against each of the two forwards. During this time his starting small forward played 25 game and his opponents averaged 18 points per game. The starting power forward played 30 games and his opponents averaged 22 points. The population standard deviation for small forwards is 4 points and the population standard deviation for power forwards is 7 points. Does the team have a weak side? With a significance level of .05 can we conclude that the two forwards have a different number of points scored against them?
What is the null hypothesis?
What is the alternative hypothesis?
What test statistic should you use?
Z-score
t stat
F distribution
p-value
What is the calculated value of the test statistics?
What is the critical value of the test statistic?
What decision should you come to?
Reject the null hypothesis
Fail to reject the null hypothesis
reject the alternative hypothesis
fail to reject the alternative hypothesis
Interpret the results:
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![\"An](\"//d2vlcm61l7u1fs.cloudfront.net/bbcswebdav/pid-1061371-dt-content-rid-3391254_1/xid-3391254_1\")
![\"An](\"//d2vlcm61l7u1fs.cloudfront.net/bbcswebdav/pid-1061371-dt-content-rid-3391255_1/xid-3391255_1\")
![\"An](\"//d2vlcm61l7u1fs.cloudfront.net/bbcswebdav/pid-1061371-dt-content-rid-3391256_1/xid-3391256_1\")
![\"An](\"//d2vlcm61l7u1fs.cloudfront.net/bbcswebdav/pid-1061371-dt-content-rid-3391257_1/xid-3391257_1\")
![\"An](\"//d2vlcm61l7u1fs.cloudfront.net/bbcswebdav/pid-1061371-dt-content-rid-3391258_1/xid-3391258_1\")
![\"An](\"//d2vlcm61l7u1fs.cloudfront.net/bbcswebdav/pid-1061371-dt-content-rid-3391259_1/xid-3391259_1\")
Solution
What is the null hypothesis?
x with bar on top subscripts equal x with bar on top subscript p
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What is the alternative hypothesis?
x with bar on top subscripts not equal to x with bar on top subscript p
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What test statistic should you use?
Z-score
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What is the calculated value of the test statistics?
Z=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)
=(18-22)/sqrt(4^2/25+7^2/30)
= -2.65
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What is the critical value of the test statistic?
It is a two-tailed test.
Given a=0.05, the critical values are Z(0.025) = -1.96 or 1.96 (from standard normal table)
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What decision should you come to?
Since Z=-2.65 is less than -1.96, we reject the null hypothesis.
Reject the null hypothesis
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Interpret the results:
So we can conclude that the two forwards have a different number of points scored against them
