Question

You wish to test the following claim (H1H1) at a significance level of α=0.10α=0.10.

      Ho:μ=79.9Ho:μ=79.9
      H1:μ≠79.9H1:μ≠79.9

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=331n=331 with a mean of M=80.6M=80.6 and a standard deviation of SD=8.2SD=8.2.

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 79.9.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 79.9.
• The sample data support the claim that the population mean is not equal to 79.9.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 79.9.

Answer 1

Given that

Ho:μ=79.9
      H1:μ≠79.9

And

n=331 with a mean of M=80.6 and a standard deviation of SD=8.2

T critical = T.INV.2T(alpha, n-1)

setting alpha = 0.10 and n-1 = 331 -1 = 330

t critical = T.INV.2T(0.10,330) =

Using TI 84 calculator

press stat then tests then Ttest

enter the data

press calculate

we get

test statistic = 1.553

test statistic is

• in the critical region

test statistic leads to a decision to...

• fail to reject the null (because test statistic is insignificant)

There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 79.9.