You wish to test the following claim (HaHa) at a significance
level of α=0.05α0.05.
Ho:μ=81.4Hoμ81.4
Ha:μ>81.4Haμ81.4
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=67n67
with mean M=87.9M87.9 and a standard deviation of
SD=20.4SD20.4.
What is the test statistic for this sample? (Report answer accurate
to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to
four decimal places.)
p-value =
The p-value is...
This test statistic leads to a decision to...
As such, the final conclusion is that...
What is the test statistic for this sample?
The test statistic formula is given as below:
t = (Xbar - µ)/[S/sqrt(n)]
From given data, we have
µ = 81.4
Xbar = 87.9
S = 20.4
n = 67
α = 0.05
t = (Xbar - µ)/[S/sqrt(n)]
t = (87.9 - 81.4)/[20.4/sqrt(67)]
t = 2.608
What is the p-value for this sample?
df = n – 1 = 66
P-value = 0.0056
(by using t-table)
The p-value is less than α.
This test statistic leads to a decision to...
reject the null
As such, the final conclusion is that...
There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 81.4.
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