Question

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

      Ho:μ=67.9Ho:μ=67.9
      Ha:μ<67.9Ha:μ<67.9

You believe the population is normally distributed and you know the standard deviation is σ=10.2σ=10.2. You obtain a sample mean of M=64.7M=64.7 for a sample of size n=36n=36.

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 less than 67.9.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 67.9.
• The sample data support the claim that the population mean is less than 67.9.
• There is not sufficient sample evidence to support the claim that the population mean is less than 67.9.

Answer 1

The hypotheses are:
Ho:μ=67.9
Ha:μ<67.9

This is a one-sample z-test as the population standard deviation is known.
σ=10.2
M = 64.7

At alpha = 0.001, the one-tailed z-critical value = -3.09

Test statistic = (M - 67.9)/(σ/√n)
= (64.7 - 67.9)/(10.2/6) = -1.882

The test statistic is not in the critical region as -1.882>-3.09

We fail to reject the null hypothesis.

The final conclusion is that:
There is not sufficient sample evidence to support the claim that the population mean is less than 67.9