Question

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

      H0:μ=76.8H0:μ=76.8
      H1:μ≠76.8H1:μ≠76.8

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=23n=23 with mean ¯x=85.9x¯=85.9 and a standard deviation of s=13.2s=13.2.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

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 76.8.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 76.8.
• The sample data support the claim that the population mean is not equal to 76.8.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 76.8.

Answer 1

Test statistic

                    

                     = 3.306

df = 23 - 1 = 22

p-value = 2 * P(T > 3.306) = 2 * 0.0016 = 0.0032

p-value is Option-A) less than (or equal to) α

This test statistic leads to a decision to Option-A) Rejects the null

Option-C) The sample data support the claim that the population mean is not equal to 76.8