Question

You have been tasked with leading the sponsorship campaign for the 250 Anniversary of the Founding of Huntsville by your bosses at Nuka-Cola Corporation. You want to use the slogan "Sponsored by Nuka-Cola, Huntsville's Bestselling Soda!". However, before you do so you want to make sure these claims are accurate. So, you go around to local grocery stores and ask them how many units of several popular sodas they have sold in the last week. Table 3 contains your results 6. Table 3 Bottles Sold x-bar Nuka-Cola 15 1197 164 Sunset Sarsaparila 15 1068 178 Vim 15 791 367 A) Calculate the pooled variance for the difference between Nuka-Cola and Sunset Sarsaparilla. B) Construct a 95 % confidence interval for the difference between average sales of Nuka-Cola and Sunset Sarsaparilla. C) Calculate the pooled variance for the difference between Nuka-Cola and Vim! D) Construct a 95% confidence interval for the difference between average sales of Nuka-Cola and Vim! E) Test the hypothesis that the average sales of Nuka-Cola are greater than that of Sunset Sarsaparilla where a= 0.05. Report your results F) Test the hypothesis that the average sales of Nuka-Cola are greater than that of Vim! where a 0.05. Report your results G) Will you use the slogan during the celebration or not? Explain your answer.

Answer 1

Solution:

A. The pooled variance is given by:-

(n1 1)sf(n2 - 1)s S2 n1n2 2

S2 (15 1)(164)2 (15 1)(178)2 1515 2

(14) (164)(14) (178)2 2 28

29290

P

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B.Since the degrees of freedom, df =
n1n2-2
= 15 + 15 - 2 = 28 and $\alpha$/2 = 0.05/2 = 0.025 is 2.048

95% confidence interval for the difference between the average sales of Nuka-Cola and Vim is given by:-

(X1 - X2)t ta/2.df S(1/n11/n2)

(1197 - 1068) $\pm$2.048*$\sqrt{}$29290*(1/15 + 1/5)

129 $\pm$ 2.048*181.034

129 $\pm$370.83

-241.83, 499.83

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C.

The pooled variance is given by:-

(n1 1)sf(n2 - 1)s S2 n1n2 2

S2 (15 1)(164)2 (15 1)(367)2 1515 2

(14) (164)2(14) (367)2 2 28

80792.5

P

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D. Since the degrees of freedom, df =
n1n2-2
= 15 + 15 - 2 = 28 and $\alpha$/2 = 0.05/2 = 0.025 is 2.048

95% confidence interval for the difference between the average sales of Nuka-Cola and Vim is given by:-

(X1 - X2)t ta/2.df S(1/n11/n2)

(1197 - 791) $\pm$2.048*$\sqrt{}$80792.5*(1/15 + 1/5)

406 $\pm$ 2.048*146.781

406 $\pm$300.67

105.33, 706.67