Solver ... Hypothesis Testing for Two or more Samples

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20160524173602two_sample_hypothesis_test_file.xls
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Mean - INDEP

Two Sample Hypothesis Test for the Mean (Independent Samples)
Level of Significance 0.05
Group 1 Group 2
Sample Mean 100 105
Sample Size 30 40
Sample Standard Deviation 10 5
Standard Error (Computed) 1.99
Test Statistic (Computed) -2.51
Lower Crit Value Upper Crit Value p-Value Decision
Two-Tailed Test -1.9600 1.9600 0.0143 Reject the null hypothesis
H1: (m1 <> m2)
Upper-Tail Test n/a 1.6449 0.9929 Do not reject the null hypothesis
H1: (m1 > m2 OR m2 < m1)
Lower-Tail Test -1.6449 n/a 0.0071 Reject the null hypothesis
H1: (m1 < m2 OR m2 > m1)
If you REJECT the null hypothesis, conclude that H1 is true.
If you DO NOT REJECT the null hypothesis, there is insufficient evidence to conclude that H1 is true.
NEVER conclude that the null hypothesis is true (i.e., we CANNOT ACCEPT the null).
©2007 DrJimMirabella.com
&A
Also referred to as ALPHA. This is your tolerance for error; it is the probability of incorrectly rejecting the null hypothesis.
A p-value is the probability of making a type 1 error if you reject the null hypothesis. In other words, it is the probability you would be making a mistake to reject the null.
If the p-value is less than the significance level, than the risk of error is within your tolerance, so you reject the null hypothesis. If the p-value is greater, you do not reject the null because the risk is too great. Another way to look at the decision is that if the test statistic > upper critical value or < lower critical value, the null hypothesis is rejected.

Mean - INDEP (raw data)

Two Sample Hypothesis Test for the Mean (Independent Samples)
Group 1 Group 2 Level of Significance 0.05
2 3
4 7 Group 1 Group 2
9 5 Sample Mean 4.000 5.000
3 8 Sample Size 5 6
2 4 Sample Standard Deviation 2.915 2.098
3
Standard Error (Computed) 1.51
Test Statistic (Computed) -0.66
Lower Upper p-Value Decision
Crit Value Crit Value
Two-Tailed Test -2.2622 2.2622 0.5245 Do not reject the null hypothesis
H1: (m1 <> m2)
Upper-Tail Test n/a 1.8331 0.7392 Do not reject the null hypothesis
H1: (m1 > m2 OR m2 < m1)
Lower-Tail Test -1.8331 n/a 0.2608 Do not reject the null hypothesis
H1: (m1 < m2 OR m2 > m1)
If you REJECT the null hypothesis, conclude that H1 is true.
If you DO NOT REJECT the null hypothesis, there is insufficient evidence to conclude that H1 is true.
NEVER conclude that the null hypothesis is true (i.e., we CANNOT ACCEPT the null).
©2007 DrJimMirabella.com
&A
Also referred to as ALPHA. This is your tolerance for error; it is the probability of incorrectly rejecting the null hypothesis.
This is the t-test statistic computed from the raw data provided.
A p-value is the probability of making a type 1 error if you reject the null hypothesis. In other words, it is the probability you would be making a mistake to reject the null.
If the p-value is less than the significance level, than the risk of error is within your tolerance, so you reject the null hypothesis. If the p-value is greater, you do not reject the null because the risk is too great. Another way to look at the decision is that if the test statistic > upper critical value or < lower critical value, the null hypothesis is rejected.

Mean - PAIRED

Two Sample Hypothesis Test for the Mean (Paired Samples)
Item Condition 1 Condition 2 Level of Significance 0.05
1 0 0
2 0 0 Standard Error (Computed) 0.00
3 0 0 Test Statistic (Computed) 0.00
4 0 0
5 0 0 0
6 0 0
7 0 0 Lower Upper p-Value Decision
8 0 0 Crit Value Crit Value
9 0 0
10 0 0 Two-Tailed Test 0.0000 0.0000 0.0000 0
11 0 0 H1: (md <> 0), (m1 <> m2)
12 0 0
13 0 0 Upper-Tail Test n/a 0.0000 0.0000 0
14 0 0 H1: (md > 0), (m1 > m2 OR m2 < m1)
15 0 0
16 0 0 Lower-Tail Test 0.0000 n/a 0.0000 0
17 0 0 H1: (md < 0), (m1 < m2 OR m2 > m1)
18 0 0
19 0 0 If you REJECT the null hypothesis, conclude that H1 is true.
20 0 0 If you DO NOT REJECT the null hypothesis, there is insufficient evidence to conclude that H1 is true.
21 0 0 NEVER conclude that the null hypothesis is true (i.e., we CANNOT ACCEPT the null).
22 0 0
23 0 0
24 0 0
25 0 0
©2007 DrJimMirabella.com
&A
Also referred to as ALPHA. This is your tolerance for error; it is the probability of incorrectly rejecting the null hypothesis.
A p-value is the probability of making a type 1 error if you reject the null hypothesis. In other words, it is the probability you would be making a mistake to reject the null.
If the p-value is less than the significance level, than the risk of error is within your tolerance, so you reject the null hypothesis. If the p-value is greater, you do not reject the null because the risk is too great. Another way to look at the decision is that if the test statistic > upper critical value or < lower critical value, the null hypothesis is rejected.

Proportion

Two Sample Hypothesis Test for the Proportion
Level of Significance 0.05
Group 1 Group 2
Number of Successes 60 140
Sample Size 100 200
Proportion (Computed) 0.60 0.70
Average Proportion 0.6666666667
Z Test Statistic (Computed) -1.73
Lower Crit Value Upper Crit Value p-Value Decision
Two-Tailed Test -1.9600 1.9600 0.0833 Do not reject the null hypothesis
H1: (P1 <> P2)
Upper-Tail Test n/a 1.6449 0.9584 Do not reject the null hypothesis
H1: (P1 > P2 or P2 < P1)
Lower-Tail Test -1.6449 n/a 0.0416 Reject the null hypothesis
H1: (P1 < P2 or P2 > P1)
If you REJECT the null hypothesis, conclude that H1 is true.
If you DO NOT REJECT the null hypothesis, there is insufficient evidence to conclude that H1 is true.
NEVER conclude that the null hypothesis is true (i.e., we CANNOT ACCEPT the null).
©2007 DrJimMirabella.com
&A
Also referred to as ALPHA. This is your tolerance for error; it is the probability of incorrectly rejecting the null hypothesis.
A p-value is the probability of making a type 1 error if you reject the null hypothesis. In other words, it is the probability you would be making a mistake to reject the null.
If the p-value is less than the significance level, than the risk of error is within your tolerance, so you reject the null hypothesis. If the p-value is greater, you do not reject the null because the risk is too great. Another way to look at the decision is that if the test statistic > upper critical value or < lower critical value, the null hypothesis is rejected.