please answer a b and c 3. Which foams more when you pour it, Coke or Pepsi? Her

Question

please answer a b and c

3. 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 12 cans: 312.2 292.6 331.7 355.1 362.9 331.7 292.6 245.8 280.9 320.0 273.1 288.7 and here are measurements for Pepsi, based on a sample of 12 cans: 148.3 210.7 152.2 117.1 89.7 140.5 128.8 167.8 156.1 136.6 124.9 136.6 a. Calculate and interpret a 99% confidence interval for the difference in population mean volumes. b. What is your claim about the foam volumes of Coke and Pepsi. c. Suppose any difference of less than 50 ml in mean volumes is not practically significant. If you claim any difference between two drinks, is this difference practically important?

Explanation / Answer

Here first we first calculate the sample mean and sample standard deviation of volume of foam(mL) after pouring a 12-oz can of coke

Here We have to find first pooled standard deviation as we see here the population variance are equal for both the drinks

sp = sqrt [ {(n1-1)s12 + (n2-1)s22}/ (n1+ n2-2)] = sqrt [(34.6142+ 29.5542)/2 ] = 32.184

99% confidence interval = (xcoke - xpepsi) +- tcritical [sp * sqrt(1/n1 + 1/n2)]] = (307.275 - 142.442) +- t0.01,22 [32.184 * sqrt (1/12 + 1/12)]

= 164.833 +- 2.8188 * 32.184 * sqrt (1/12 + 1/12)

= 164.833 +- 37.036

= (127.78 mL, 201.87 mL)

b. Here we can claim that foam volumes of Coke is significantly higher than the foam volumers of Pepsi and it is 99% confidence that it is in between 127.78 mL to 201.87 mL

(c) Here as the confidence intervaltells that the difference is also significant greater than 50 mL also so we can see that there is very significant difference between mean volumes of two drinks.

Coke Pepsi 312.2 148.3 292.6 210.7 331.7 152.2 355.1 117.1 362.9 89.7 331.7 140.5 292.6 128.8 245.8 167.8 280.9 156.1 320 136.6 273.1 124.9 288.7 136.6 Mean 307.275 142.442 Std.Dev. 34.614 29.554

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