5. You wish to test the following claim (HaHa) at a significance level of =0.001

Question

5. You wish to test the following claim (HaHa) at a significance level of =0.001=0.001.

      Ho:=82.2Ho:=82.2
      Ha:>82.2Ha:>82.2

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=125n=125 with mean M=85.2M=85.2 and a standard deviation of SD=17.6SD=17.6.

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)

B greater than

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 82.2.

B There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 82.2.

C The sample data support the claim that the population mean is greater than 82.2.

D There is not sufficient sample evidence to support the claim that the population mean is greater than 82.2.

Explanation / Answer

Solution:

From the given info n = 125, M = 85.2, SD = 17.6
Test statistic:
Ho : = 82.2
Ha : > 82.2
Test statistic z = M - /SD/sqrt(n)
= (85.2 - 82.2) /17.6/sqrt(125)
= 1.9057
p-value = 0.0567
so, P-value is
B) greater than

This test statistic leads to a decision to
C) fail to reject the null

As such, the final conclusion is that
B)There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 82.2.

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