Homework Sourse00 00 Solutiona Let mu be the population mean Null hypothesi
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00Solution
(a) Let mu be the population mean
Null hypothesis: mu=1700
Alternative hypothesis: mu<1700
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(b)
The degree of freedom =n-1=32-1=31
Given a=0.05, the critical value is t(0.05, df=31) = -1.696 (from student t table)
The test statistic is
t=(xbar-mu)/(s/vn)
=(1650-1700)/sqrt(250/32)
=-17.89
Since t=-17.89 is less than -1.696, we reject the null hypothesis.
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(c) (Xbar-mean)/(s/vn) = -1.696
--> (Xbar- 1700)/sqrt(250/32) = -1.696
--> Xbar = 1700 -1.696*sqrt(250/32) =1695.26
So the power= P(xbar >1695.26)
=P(t with df=31>(1695.26-1692)/sqrt(250/32))
=P(t with df=31>1.17) =0.1255 (from student t table)
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(d)increase sample size.
