Question

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

      Ho:μ=80.2Ho:μ=80.2
      Ha:μ>80.2Ha:μ>80.2

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=55n=55 with mean ¯x=82.7x¯=82.7 and a standard deviation of s=5.4s=5.4.

What is the test statistic for this sample?
test statistic = (Report answer accurate to 3 decimal places.)

What is the p-value for this sample?
p-value = (Report answer accurate to 4 decimal places.)

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 greater than 80.2.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 80.2.
• The sample data support the claim that the population mean is greater than 80.2.
• There is not sufficient sample evidence to support the claim that the population mean is greater than 80.2.

Answer 1

Solution:

1)

The test statistic t is

t =   = [82.7 - 80.2]/[5.4 /55] = 3.433

test statistic = 3.433

2)

d.f. = n - 1 = 55 - 1 = 54

> sign in Ha indicates that the test is "One tailed right sided"

t = 3.433

So ,

p value = 0.0006

3)

The p-value is...

less than (or equal to) αα

4)

This test statistic leads to a decision to...

reject the null

5)

As such, the final conclusion is that...

The sample data support the claim that the population mean is greater than 80.2.