Question

You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05.

      Ho:μ≤70.8Ho:μ≤70.8
      Ha:μ>70.8Ha:μ>70.8

You believe the population is normally distributed and you know the standard deviation is σ=13.6σ=13.6. You obtain a sample mean of ¯x=74.5x¯=74.5 for a sample of size n=31n=31.

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

What is the standardized 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 70.8.

There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 70.8.

The sample data support the claim that the population mean is greater than 70.8.

There is not sufficient sample evidence to support the claim that the population mean is greater than 70.8.

Answer 1

Solution :

Given that ,

= 74.5

= 70.8

= 13.6

n = 31

= 0.05

Z = Z_0.05 = 1.65

Critical value = 1.65

Test statistic = z = ( - ) / / n

= (74.5 - 70.8) / 13.6 / 31 = 1.515

Test statistic = 1.515

Test statistic < critical value

The test statistic is not in the critical region .

Fail to reject the null hypothesis .

There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 70.8.