Which foams more when you pour it, Coke or Pepsi? Here are measurements on the f
ID: 3225763 • Letter: W
Question
Which foams more when you pour it, Coke or Pepsi? Here are measurements on the foam volume (mL) after pouring a 12-oz can of Coke, based on a sample of 10 cans; as well as measurements for Pepsi, based on a sample of 10 cans:
(a) Obtain a 99% two-sided condence interval for the population dierence between the two means and interpret it in terms of the relationship between the foam volumes of Coke and Pepsi under the following assumptions.
i. The Coke sample is independent of the Pepsi sample.
ii. Both samples are drawn from normally distributed populations with equal variances.
(b) Obtain a 99% two-sided condence interval for the population dierence between the two means and interpret it in terms of the relationship between the foam volumes of Coke and Pepsi under the following assumptions.
i. The two samples are actually paired (dependent).
ii. The dierences are drawn from a normally distributed population.
1 2 3 4 5 6 7 8 9 10 mean st. dev. Coke 312 293 332 355 363 332 293 246 281 321 312.8 35.53 Pepsi 148 211 152 117 90 141 129 168 156 137 144.9 31.99 differences 164 82 180 238 273 191 164 78 125 184 167.9 61.67Explanation / Answer
a.
Two-Sample T-Test and CI: Coke, Pepsi
Two-sample T for Coke vs Pepsi
SE
N Mean StDev Mean
Coke 10 312.8 35.5 11
Pepsi 10 144.9 32.0 10
Difference = (Coke) - (Pepsi)
Estimate for difference: 167.9
99% CI for difference: (124.4, 211.4)
T-Test of difference = 0 (vs ): T-Value = 11.11 P-Value = 0.000 DF = 18
Both use Pooled StDev = 33.8071
b.
Paired T-Test and CI: Coke, Pepsi
Paired T for Coke - Pepsi
N Mean StDev SE Mean
Coke 10 312.8 35.5 11.2
Pepsi 10 144.9 32.0 10.1
Difference 10 167.9 61.7 19.5
99% CI for mean difference: (104.5, 231.3)
T-Test of mean difference = 0 (vs 0): T-Value = 8.61 P-Value = 0.000
In both the results we can say P-value <0.01, We reject null hypothesis.
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