A postmix beverage machine is adjusted to release a certain amount of syrup into a chamber where it is mixed with carbonated water. A random sample of 25 beverages was found to have a mean syrup content of x = 1.0 fluid ounces and a standard deviation of s = 0.020 fluid ounces. Assume population is approximately normally distributed. Compute a 95% prediction interval on the syrup volume in the next beverage dispensed. Compare the length of the prediction interval with the length of the 95% confidence interval on the population mean. Round your answers to 3 decimal places. i ≤Xn+1 ≤ i

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A postmix beverage machine is adjusted to release a certain amount of syrup into a chamber where it is mixed with carbonated water. A random sample of 25 beverages was found to have a mean syrup content of \(\bar{x} = 1.0\) fluid ounces and a standard deviation of \(s = 0.020\) fluid ounces. Assume the population is approximately normally distributed.

Compute a 95% prediction interval on the syrup volume in the next beverage dispensed. Compare the length of the prediction interval with the length of the 95% confidence interval on the population mean.

Round your answers to 3 decimal places.

\[ \text{[ ]} \leq x_{n+1} \leq \text{[ ]} \]

The 95% prediction interval is \(\_\_\_\_\_\_\_\_\_\_\) the 95% confidence interval.
Transcribed Image Text:A postmix beverage machine is adjusted to release a certain amount of syrup into a chamber where it is mixed with carbonated water. A random sample of 25 beverages was found to have a mean syrup content of \(\bar{x} = 1.0\) fluid ounces and a standard deviation of \(s = 0.020\) fluid ounces. Assume the population is approximately normally distributed. Compute a 95% prediction interval on the syrup volume in the next beverage dispensed. Compare the length of the prediction interval with the length of the 95% confidence interval on the population mean. Round your answers to 3 decimal places. \[ \text{[ ]} \leq x_{n+1} \leq \text{[ ]} \] The 95% prediction interval is \(\_\_\_\_\_\_\_\_\_\_\) the 95% confidence interval.
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