Question

# You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001.       Ho:μ=82.7Ho:μ=82.7       Ha:μ≠82.7Ha:μ≠82.7...

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

Ho:μ=82.7Ho:μ=82.7
Ha:μ≠82.7Ha:μ≠82.7

You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

data
64.6
58.1
60.1
58.1
78.6
71.2
60.6
86.9
75.2
88.3
77.1

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value = ±±

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

The test statistic is...

• in the critical region
• not in the critical region

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 82.7.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 82.7.
• The sample data support the claim that the population mean is not equal to 82.7.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 82.7.

The statistical software output for this problem is : critical value = ± 4.587

test statistic = -3.509

The test statistic is not in the critical region .

fail to reject the null

There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 82.7.