Question

You wish to test the following claim (HaHa) at a significance level of α=0.005α=0.005.

      Ho:μ=73.7Ho:μ=73.7
      Ha:μ≠73.7Ha:μ≠73.7

You believe the population is normally distributed and you know the standard deviation is σ=15.8σ=15.8. You obtain a sample mean of M=67.7M=67.7 for a sample of size n=44n=44.

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 73.7.

There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 73.7.

The sample data support the claim that the population mean is not equal to 73.7.

There is not sufficient sample evidence to support the claim that the population mean is not equal to 73.7.

Answer 1

Solution :

Given that,

= 67.7

= 73.7

= 15.8

n = 44

= 0.005

/ 2 = 0.005 / 2 = 0.0025

Z_/2 = Z_0.0025 = 2.81

Critical value = 2.807

Test statistic = z = ( - ) / / n

= (67.7 - 73.7) / 15.8 / 44 = -2.519

Test statistic = -2.519

Test statistic > critical value

The test statistic is in the critical region .

Reject the null hypothesis .

There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 73.7