The accompanying data set includes volumes (ounces) of a sample of cans of regular Coke. The summary statistics are $n=36, \bar{x}=12.190 \mathrm{oz}, \mathrm{s}=0.111 \mathrm{oz}$. Assume that a simple random sample has been selected. Use a 0.01 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? 进
Identify the null and alternative hypotheses.
(Type integers or decimals. Do not round.)
Identify the test statistic.
(Round to two decimal places as needed)
Identify the P-value.
(Round to three decimal places as needed.)
State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Decide whether it appears that consumers are being cheated.
the null hypothesis. There sufficient evidence at the 0.01 significance level to the claim that cans of Coke have a mean volume of 12.00 ounces. It that Gonsumers are being cheated, because consumers are getting 12.00 ounces.

Step 1 ：Set up the null and alternative hypotheses. The null hypothesis (H0) is that the mean volume of cans of Coke is 12.00 ounces. The alternative hypothesis (H1) is that the mean volume is not 12.00 ounces.

Step 2 ：Calculate the test statistic using the formula for the z-score, which is \((\bar{x} - \mu) / (s / \sqrt{n})\).

Step 3 ：Find the P-value. The P-value is the probability of obtaining a result as extreme as the one that was actually observed, assuming that the null hypothesis is true.

Step 4 ：If the P-value is less than the significance level (0.01 in this case), reject the null hypothesis.

Step 5 ：Make a conclusion based on the findings. If the null hypothesis is rejected, this means that there is sufficient evidence to support the claim that the mean volume of cans of Coke is not 12.00 ounces. If the null hypothesis is not rejected, this means that there is not enough evidence to support the claim that the mean volume is not 12.00 ounces.

Step 6 ：Given the sample mean is greater than the claimed mean, it does not appear that consumers are being cheated. In fact, they are getting slightly more Coke than advertised on average.

Step 7 ：Final Answer: The null hypothesis is that the mean volume of cans of Coke is 12.00 ounces. The alternative hypothesis is that the mean volume is not 12.00 ounces. The test statistic is approximately 10.27 and the P-value is 0. Therefore, we reject the null hypothesis. There is sufficient evidence at the 0.01 significance level to support the claim that cans of Coke have a mean volume different from 12.00 ounces. It does not appear that consumers are being cheated, as they are getting slightly more Coke than advertised on average. So, the final answer is: Null and alternative hypotheses: \(H_0: \mu = 12.00\) ounces, \(H_1: \mu \neq 12.00\) ounces Test statistic: \(z \approx 10.27\) P-value: \(p = 0.0\) Conclusion: We reject the null hypothesis. There is sufficient evidence at the 0.01 significance level to support the claim that cans of Coke have a mean volume different from 12.00 ounces. It does not appear that consumers are being cheated. \(\boxed{\text{Final Answer}}\)