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.
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.