Following is a sample of 5 mathched pairs.Sample 1  19 15  16  23  24Sample 2  18  19  10  14  17let u1 and u2 represent the population means and let ud=u1-u2. A test will be made of the hypothesis Ho: ud=0 versus H1:Ud greater 0.a. Compute the differences.b. Compute the test statisticc. Can you reject H0 at the a= 0.05 level of significance?d. Can you reject H0 at the a=0.01 level of significance?

Question
Asked Nov 17, 2019
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Following is a sample of 5 mathched pairs.

Sample 1  19 15  16  23  24

Sample 2  18  19  10  14  17

let u1 and u2 represent the population means and let ud=u1-u2. A test will be made of the hypothesis Ho: ud=0 versus H1:Ud greater 0.

a. Compute the differences.

b. Compute the test statistic

c. Can you reject H0 at the a= 0.05 level of significance?

d. Can you reject H0 at the a=0.01 level of significance?

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Expert Answer

Step 1

(a)

The differences is,

Sample 1 Sample 2 Difference
19
18
19-18-1
15
19
15-19-4
16
10
16-10-6
23
14
23-14-9
24
17
24-17-7
Total
19
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Sample 1 Sample 2 Difference 19 18 19-18-1 15 19 15-19-4 16 10 16-10-6 23 14 23-14-9 24 17 24-17-7 Total 19

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Step 2

(b)

Step-by-step procedure to obtain the p-value and test statistic using MINITAB software:

  • Choose Stat > Basic Statistics > Paired t.
  • Choose Samples in different columns.
  • In sample 1, enter the column of Sample 1.
  • In sample 2, enter the column of Sample 2.
  • Choose Options.
  • In Confidence level, enter 95.
  • In Hypothesized difference, enter 0.
  • In Alternative, select greater than.
  • Click OK in all the dialogue boxes.

The output obtained using MINITAB software is given below:

Paired T-Test and Cl: Sample 1, Sample 2
Descriptive Statistics
Sample N Mean StDev SE Mean
1.8
Sample 1 5 19.40
Sample 2 5 15.60
4.04
3.65
1.63
Estimation for Paired Difference
95% Lower Bound
for difference
Mean StDev SE Mean
3.80
5.26
2.35
-1.22
difference: mean of (Sample 1-Sample 2)
Test
Ho _difference o
Null hypothesis
Alternative hypothesis H:difference 0
T-Value P-Value
1.61
0.091
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Paired T-Test and Cl: Sample 1, Sample 2 Descriptive Statistics Sample N Mean StDev SE Mean 1.8 Sample 1 5 19.40 Sample 2 5 15.60 4.04 3.65 1.63 Estimation for Paired Difference 95% Lower Bound for difference Mean StDev SE Mean 3.80 5.26 2.35 -1.22 difference: mean of (Sample 1-Sample 2) Test Ho _difference o Null hypothesis Alternative hypothesis H:difference 0 T-Value P-Value 1.61 0.091

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Step 3

Thus, the test statistic is 1.61.

(c)

Rejectio...

If p-value significance level, reject the null hypothesis.
If p-value significance level, do not reject the null hypothesis
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If p-value significance level, reject the null hypothesis. If p-value significance level, do not reject the null hypothesis

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