Question

You wish to test the following claim (H1H1) at a significance level of α=0.001α=0.001.

      Ho:μ=82.3Ho:μ=82.3
      H1:μ>82.3H1:μ>82.3

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=26n=26 with a mean of ¯x=90x¯=90 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 82.3.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 82.3.
• The sample data support the claim that the population mean is greater than 82.3.
• There is not sufficient sample evidence to support the claim that the population mean is greater than 82.3.

Answer 1

Given that, sample size (n) = 26, sample mean = 90 and

sample standard deviation (s) = 11.9

The null and alternative hypotheses are,

H0 : μ = 82.3

H1 : μ > 82.3

This test is right-tailed test,

Degrees of freedom = 26 - 1 = 25

t-critical value at significance level of 0.001 is, t* = 3.450

=> Critical value = 3.450

Test statistic is,

=> test statistic = 3.299

Since, test statistic = 3.299 < 3.450,

The test statistic is not in the critical region.

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

As such, the final conclusion is that, There is not sufficient sample evidence to support the claim that the population mean is greater than 82.3.