Question

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

      Ho:μ=72.9Ho:μ=72.9
      Ha:μ>72.9Ha:μ>72.9

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=337n=337 with a mean of M=73.4M=73.4 and a standard deviation of SD=19.3SD=19.3.

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 greater than 72.9.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 72.9.
• The sample data support the claim that the population mean is greater than 72.9.
• There is not sufficient sample evidence to support the claim that the population mean is greater than 72.9.

Answer 1

Solution:

1)What is the critical value for this test?

Observe the alternative hypothesis Ha:μ > 72.9

Right tailed test

α=0.002 given .

n = 337

df = n - 1 = 337 - 1 = 336

Critical value for the right tailed test is

critical value = 2.898

2) What is the test statistic for this sample?

t =  

= (73.4 - 72.9)/(19.3/337)

= 0.476

test statistic = 0.476

3)The test statistic is...

fail to reject the null

4)

As such, the final conclusion is that...

There is not sufficient sample evidence to support the claim that the population mean is greater than 72.9.