(1) null hypothesis
H0:µwalmart=µbounty and
alternate hypothesis H1:µwalmart ?
µbounty
(2) level of significance (alpha)=0.10
(3)here we use t-test with
(4) reject H0 if t > 1.729
the two tailed critical value is t(0.1/2,19)=1.729
(5)statistic t=|(mean1-mean2)|/((sp*(1/n1
+1/n2)1/2) =2.7224
with df is n=n1+n2-2 =19and
sp2=((n1-1)s12+(n2-1)s22)/n=6.1623
since the calculated t=2.7224 belongs to critical region , so we
reject the null hypothesis
(or p-value is less than level of significance alpha=0.1, so we
reject H0)
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t-test |
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sample |
mean |
s |
s2 |
n |
(n-1)s2 |
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walmart |
6.4400 |
3.3200 |
11.0224 |
9 |
88.1792 |
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bounty |
9.4200 |
1.6210 |
2.6276 |
12 |
28.9041 |
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difference= |
2.9800 |
sum= |
13.6500 |
21 |
117.0833 |
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sp2= |
6.1623 |
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sp= |
2.4824 |
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SE= |
1.0946 |
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t= |
2.7224 |
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two tailed |
p-value= |
0.0135 |
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two tailed critical |
t(0.1/2) |
1.7291 |
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(6) since we reject the null hypothesis and we may interpret
as there is a difference in the mean amount of liquid
absorbed by the two paper towels.
