Question

# You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002.       Ho:μ=86.2Ho:μ=86.2       Ha:μ>86.2Ha:μ>86.2...

You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002.

Ho:μ=86.2Ho:μ=86.2
Ha:μ>86.2Ha:μ>86.2

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=14n=14with mean M=103.2M=103.2 and a standard deviation of SD=16.7SD=16.7.

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...

A) less than (or equal to) α

or

B) greater than α

This test statistic leads to a decision to...

A) reject the null

B) accept the null

C) fail to reject the null

As such, the final conclusion is that...

A) There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 86.2.

B) There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 86.2.

C) The sample data support the claim that the population mean is greater than 86.2.

D) There is not sufficient sample evidence to support the claim that the population mean is greater than 86.2.

Solution:

Test Hypothesis :
Ho : μ = 86.2
Ha : μ > 86.2
α = 0.02
Standard deviation SD = 13.3
Sample mean M = 103.2
Sample size n = 14

Test Statistic : Z = (M - μ)/(SD/√n)
= (103.2-86.2)/(13.3/√14)
= 17/3.55
= 4.7887
---------------------------------------------------------------------------
being a right tailed test, p-value = P(Z > 4.7887) = 0
α = 0.02
As p-value : 0 < α : 0.02 Reject null hypothesis.

The p-value is
B) greater than α
---------------------------------------------------------
This test statistic leads to a decision to...
A) reject the null
---------------------------------------------------------
As such, the final conclusion is that...
A) There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 86.2.

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