Question

You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002.

      Ho:μ1=μ2Ho:μ1=μ2
      Ha:μ1<μ2Ha:μ1<μ2

You obtain the following two samples of data.

Sample #1	Sample #2
78.5 66.6 90.1 69.7 76.1 82.9 78.7 77.3 84.8 71 76.9 92.5 65.2 71.7 76.5 63.3 66.6 76.9 74.7 85.2 81.1 84.5 91.2 75.5 76.1 73.3 89.3 69.9 57.9 69.1 82.7 71.9 70.2 89.3 79.3 73.9 65.2	73.9 83.2 74.4 80.3 69.5 81.8 78 94.8 67 91.1 89.2 80.2 73.9 85 81.8 85.4 78.5 78.7 82.6 77.2 81.1 88 78.3 89.6 85.2 71.9 80.2 78.7 78.9 83.6 88 84.3 80.7 70.4 66.1 72.8 70 78.7 88 89.6 80.7 85.4 80.5 76.6 62.8 84.1 80.3 80.7 73.4 79.8

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? For this calculation, use the degrees of freedom reported from the technology you are using. (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 first population mean is less than the second population mean.

There is not sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean.

The sample data support the claim that the first population mean is less than the second population mean.

There is not sufficient sample evidence to support the claim that the first population mean is less than the second population mean.

Answer 1

The statistical software output for this problem is:

Two sample T hypothesis test:
μ₁ : Mean of Sample 1
μ₂ : Mean of Sample 2
μ₁ - μ₂ : Difference between two means
H₀ : μ₁ - μ₂ = 0
H_A : μ₁ - μ₂ < 0
(without pooled variances)

Hypothesis test results:

Difference	Sample Diff.	Std. Err.	DF	T-Stat	P-value
μ1 - μ2	-3.5304324	1.6859326	67.304786	-2.0940531	0.02

Hence,

Test statistic = -2.094

p - Value = 0.0200

greater than α

fail to reject the null

There is not sufficient sample evidence to support the claim that the first population mean is less than the second population mean. Option D is correct.