Question

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

      Ho:μ=81.1Ho:μ=81.1
      Ha:μ>81.1Ha:μ>81.1

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=751n=751 with a mean of M=82M=82 and a standard deviation of SD=11.9SD=11.9.

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 81.1.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 81.1.
• The sample data support the claim that the population mean is greater than 81.1.
• There is not sufficient sample evidence to support the claim that the population mean is greater than 81.1

Answer 1

Solution :

Given that ,

= 82

= 81.1

= 11.9

n = 50

= 0.001

Z = Z_0.001 = 3.09

Critical value = 3.09

Test statistic = z

= ( - ) / / n

= (82 - 81.1) / 11.9 / 50

= 0.535

Test statistic = 0.535

The test statistic is not in the critical region

Test statistic < critical value

Fail to reject the null hypothesis .

There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 81.1.