Question 141841: On eight Friday quizzes, Bob received scores of 80, 85, 95, 92, 89, 84, 90, 92. He tells Prof.
Hardtack that he is really a 90+ performer but this sample just happened to fall below his true
performance level. (a) State an appropriate pair of hypotheses. (b) State the formula for the test
statistic and show your decision rule using the 1 percent level of significance. (c) Carry out the
test. Show your work. (d) What assumptions are required? (e) Use Excel to find the p-value and
interpret it.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! On eight Friday quizzes, Bob received scores of 80, 85, 95, 92, 89, 84, 90, 92. He tells Prof. Hardtack that he is really a 90+ performer but this sample just happened to fall below his true performance level.
(a) State an appropriate pair of hypotheses.
Ho: u>= 90
H1: u < 90
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(b) State the formula for the test statistic and show your decision rule using
the 1 percent level of significance.
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Critical value for df= 7 and alpha=1% : t=-2.998
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Find the sample mean: 88.375
and standard deviation: 4.9839
(c) Carry out the test. Show your work.
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t(88.375) = (88.375-90)/[4.9839/sqrt(8)] = -0.9222...
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(d) What assumptions are required?
Check in your textbook
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(e) Use Excel to find the p-value and interpret it.
p-value = P(-10 < t < -0.9222) = 0.1935..
The probability the test results could have given stronger evidence
for rejecting Ho is 19.35%; therefore fail to reject Ho.
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cheers,
Stan H.
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