You wish to test the following claim (HaHa) at a significance
level of α=0.05α=0.05.
Ho:μ≤86.2Ho:μ≤86.2
Ha:μ>86.2Ha:μ>86.2
You believe the population is normally distributed and you know the
standard deviation is σ=16.8σ=16.8. You obtain a sample mean of
¯x=89x¯=89 for a sample of size n=72n=72.
What is the test statistic for this sample? (Report the 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... Select an answer less than (or equal to) α
greater than α
This test statistic leads to a decision to... Select an answer
reject the null accept the null fail to reject the
null hypothesis.
As such, the conclusion is that... Select an answer At the 5%
significance level, the data provides sufficent evidence to support
the claim that the μ > 86.2. At the 5% significance level, the
data provides insufficient evidence to support the claim that the μ
> 86.2.
Solution :
This is the right tailed test,
The null and alternative hypothesis is ,
H0 : 86.2
Ha : > 86.2
Test statistic = z =
= ( - ) / / n
= (89 - 86.2) / 16.8 / 72
Test statistic = z = 1.414
P(Z > 1.414) = 1-P (Z < 1.414) = 1 - 0.9213
P-value = 0.0787
α = 0.05
The p-value is greater than α .
This test statistic leads to a decision to fail to reject the null hypothesis.
At the 5% significance level, the data provides insufficient evidence to support the claim that the μ > 86.2
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