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ID: 3363174 • Letter: N
Question
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a) This is the dependent test.
b) Here we have to test the hypothesis that,
H0 : Mud = 0 Vs H1 : Mud not= 0
where Mud is population mean difference between below and above.
Assume alpha = level of significance = 5% = 0.05
c) We use paired t-test.
Here test statistic follows t-distribution with n-1 degrees of freedom.
We can dopaired t test in MINITAB.
steps :
ENTER data into MINITAB sheet --> Stat --> Basic statistics --> Paired t --> Samples in columns --> First sample : select below data --> Second sample : select above data --> Options --> Confidence level : 95.0 --> Test mean : 0.0 --> Alternative : not equal --> ok --> ok
Welcome to Minitab, press F1 for help.
Paired T-Test and CI: below, above
Paired T for below - above
N Mean StDev SE Mean
below 8 7.00 3.12 1.10
above 8 9.00 3.78 1.34
Difference 8 -2.000 1.927 0.681
95% CI for mean difference: (-3.612, -0.388)
T-Test of mean difference = 0 (vs not = 0): T-Value = -2.94 P-Value = 0.022
Test statistic = -2.94
P-value = 0.022
P-value < alpha
Reject H0 at 5% level of significance.
Conclusion : The population mean difference is differ than 0.
d) 95% confidence interval for mean difference is (-3.612, -0.388).
99% confidence interval for mean difference is (-4.385, 0.385).
e) Cohen's d :
Cohen's d = Xbar - mud / sigma = -2/1.927 = -1.04
Distance is always positive so Cohen's d = 1.04
So Cohen's d > 0.6 therefore large effect size.
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