The reaction time for a random group of n = 10 sober college students was measur
ID: 3156504 • Letter: T
Question
The reaction time for a random group of n = 10 sober college students was measured one-half hour prior to consuming three cans of beer and one-half hour afterwards. The reaction times measured in hundreds of a second are as follows (study presented in Basic Statistics for the Social Sciences by Glass and Hopkins (1995). Test to see if the “before” reaction times are less than the “after” reaction times.
Student
1
2
3
4
5
6
7
8
9
10
Before:
15
9
10
7
12
15
9
10
13
11
After:
20
25
15
10
16
26
15
16
20
18
Ho: Ha:
Degrees of freedom, Critical Value(s)/rejection region(s):
Test Statistic:
P-value:
Decision and conclusion:
Student
1
2
3
4
5
6
7
8
9
10
Before:
15
9
10
7
12
15
9
10
13
11
After:
20
25
15
10
16
26
15
16
20
18
Explanation / Answer
Here we have to test the hypothesis that,
H0 : mu1 = mu2 Vs H1 : mu1 < mu2
Where mu1 is population mean for before.
mu2 is population mean for after.
Assume alpha = level of significance = 5% = 0.05
Here the samples are paired and one observation for two samples.
Here we use paired test.
We can done Paired t-test using MINITAB.
steps :
Enter all the data in MINITAB sheet --> Stat --> Basic statistics --> Paired t (Test and Confidence Interval) --> Samples in columns --> First sample : select first sample --> second sample : select second sample --> Options --> COnfidence level : 95.0 --> Test mean : 0 --> Alternative : select less than option --> ok --> ok
Output is :
Paired T for before - after
N Mean StDev SE Mean
before 10 11.1000 2.6437 0.8360
after 10 18.1000 4.8408 1.5308
Difference 10 -7.00000 3.82971 1.21106
95% upper bound for mean difference: -4.77999
T-Test of mean difference = 0 (vs < 0): T-Value = -5.78 P-Value = 0.000
Test statistic t = -5.78
P-value = 0.000
P-value < alpha
Reject H0 at 5% level of significance.
Conclusion : There is sufficient evidence to say that the “before” reaction times are less than the “after” reaction times.
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