8 5 points Test the given claim using the \( P \)-value method method. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. The claim is that Coke and Pepsi cans have the same mean volume. Volumes of cans of regular Coke and volumes of cans of regular Pepsi are listed below. \begin{tabular}{|l|l|l|l|} \hline Coke & \( n=36 \) & \( \bar{x}=12.19 \) & \( s=0.11 \) ounces \\ \hline Pepsi & \( n=36 \) & \( \bar{x}=12.29 \) & \( s=0.09 \) ounces \\ \hline \end{tabular} Null Hypothesis: type your answer... Alternative Hypothesis: type your answer... Test Statistic: type your answer... P-value: typeyour answer... Null Conclusion: choose your answer.. Final Conclusion: type your answer.. 9 \( \$ \) points
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Mathematically, \(H_0: \mu_{\text{Coke}} = \mu_{\text{Pepsi}}\). - Alternative Hypothesis (\(H_a\)): The mean volume of Coke cans is not equal to the mean volume of Pepsi cans. Mathematically, \(H_a: \mu_{\text{Coke}} \neq \mu_{\text{Pepsi}}\). Show more…
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Assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim. Data Set 26 "Cola Weights and Volumes" in Appendix B includes volumes (ounces) of a sample of cans of regular Coke. The summary statistics are $n=36, \bar{x}=12.19$ oz, $s=0.11$ oz. Use a 0.05 significance level to test the claim that cans of Coke have a mean volume of 12.00 ounces. Does it appear that consumers are being cheated?
Hypothesis Testing
Testing a Claim About a Mean
Testing Hypotheses. In Exercises $5-18,$ test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, $P$ -value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the $P$ -value method unless your instructor specifies otherwise. Cans of Coke A simple random sample of 36 cans of regular Coke has a mean volume of 12.19 oz (based on Data Set 17 in Appendix B). Assume that the standard deviation of all ans of regular Coke is 0.11 oz Use a 0.01 significance level to test the claim that cans of regular Coke have volume with a mean of 12 oz, as stated on the labcl. If there is a difference, is it substantial?
Testing a Claim About a Mean: $\sigma$ Known
Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9 - 1 along with "Table" answers based on Table $A$ - 3 with df equal to the smaller of $\boldsymbol{n}_{I}-\boldsymbol{I}$ and $\boldsymbol{n}_{2}-\boldsymbol{I} .$ ) Coke and Pepsi Data Set 26 "Cola Weights and Volumes" in Appendix B includes volumes of the contents of cans of regular Coke $(n=36, \bar{x}=12.19 \text { oz, } s=0.11$ oz ) and volumes of the contents of cans of regular Pepsi $(n=36, \bar{x}=12.29 \text { oz, } s=0.09$ oz). a. Use a 0.05 significance level to test the claim that cans of regular Coke and regular Pepsi have the same mean volume. b. Construct the confidence interval appropriate for the hypothesis test in part (a). c. What do you conclude? Does there appear to be a difference? Is there practical significance?
Inferences from Two Samples
Two Means: Independent Samples
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