IGNORE #8! #13: \"What is the power of the test at the level 0.5 if the mean u i

Question

IGNORE #8!
#13: "What is the power of the test at the level 0.5 if the mean u is 100" (not in picture).

Further info attached in top photo.
Thank you!

In the last question, take the null hypothesis to be that mu 100. The test is to reject if the sample mean x bar exceeds 100 1.645(3.2) 100+ 5.264 105.264, since 3.2 is the standard error of the mean The "power" when mu 110 is the probability of rejecting this hypothesis, assuming that the true mean is 110. So it is the probability that the sample mean X-bar exceeos 105.264, when mu 110 This will be a high probability. To compute this probability, convert 105.264 to a z score

Explanation / Answer

Solution7:

sample standard deviation=sigma/sqrt(n)

=16/sqrt(25)

=16/5

=3.2

standard deviatin of sample mean=3.2

Solution9:

P(X bar>110)

z=x-mean/sample sd

=110-100/3.2

=10/3.2

using R software:

pnorm(3.125,mean=0,sd=1,lower.tail = FALSE)

=0.0008890253

ANSWER:

P(xbar>110)=0.00089

z=3.125

Solution10:

qnorm(0.95)

1.644854

z score for 95 th percentile=1.644854

z=x-mean/sd

1.644854=x-100/3.2

x=1.644854*3.2+100

x=105.2635

ANSWER:105.2635

Solution13:

beta=P(Z<-1.64-0.5*sqrt(25)

beta=P(Z<-0.86)

beta=0.1949

power=1-beta

=1-0.1949

=0.8051

=0.8051*100

power =80.51%

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