Question

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

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

You obtain the following two samples of data.

Sample #1

Sample #2

63.6	29.4	22	70.8
78.8	36.9	62	55.7
46.7	60.4	25.4	57.8
53.6	65.3	56.7	43.8
43.8	68.9	55.7	103.4
59.3	51	76.9	60.9
19.8	35.3	84.5	59.8
91.6	66.5	47.8	78.8
58.3	8	51.6	55.2
97.8	60.9	70.8	60.4
41.9	42.5	49.4	35.3
40.6	38.4	78.8	71.5
32.6	31.6	66.5	41.9
56.7	37.7	58.3	55.7
64.7	67.6	44.9	80.8
36.1	65.3	53.1	97.8
74.5

48.6	56.2	89.6	73.6
69.7	60.7	54.1	63.9
44.1	51.7	53.2	55.8
86.5	89.6	65.9	38.6
61.1	73.6	82.1	48.6
79.7	65.5	91.6	43.3
43.3	83.1	37.3	86.5
54.5	61.1	80.5	54.1
48.6	65.9	72.1	89.6
86.5	79.7	70.2	83.1
61.5	81.3	61.5	63.9
51.2

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

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

t-Test: Two-Sample Assuming Unequal Variances
	Sample #1	Sample #2
Mean	56.30923	65.84
Variance	371.1209	244.4361
Observations	65	45
Hypothesized Mean Difference	0
df	105	Degree of freedom
t Stat	-2.855	Test -stats
P(T<=t) one-tail	0.0026	P-value
t Critical one-tail	3.16967
P(T<=t) two-tail	0.005182
t Critical two-tail	3.385608

P-value is GREATER than

FAIL TO REJECT THE NULL

• There is sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean.