Question

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

      Ho:μ=86.1Ho:μ=86.1
      Ha:μ≠86.1Ha:μ≠86.1

You believe the population is normally distributed and you know the standard deviation is σ=14.2σ=14.2. You obtain a sample mean of M=84.5M=84.5 for a sample of size n=63n=63.

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 86.1.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 86.1.
• The sample data support the claim that the population mean is not equal to 86.1.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 86.1.

Answer 1

Here we have to test that

,

n = 63

Here population standard deviation is known and population is normally distributed so we will use here z test.

alpha = 0.05

left area = right area = 0.025

Middle area = 0.95

z critical for (1+0.95)/ = 0.975 is

z critical = 1.96                        (From statistical table of z values)

Critical value = 1.96

Test statistic:

z = -0.894                     (Round to 3 decimal)

Test statistic = - 0.894

Test is two tailed test.

Here |test statistic| = |-0.894| = 0.894 < critical value = 1.96

So test statistic is in the critical region.

This test statistic leads to a decision to fail to reject the null hypothesis H0.

Conclusion: There is not sufficient sample evidence to support the claim that the population mean is not equal to 86.1.