Explanation:
To construct a confidence interval for the mean number of ounces of juice bottled by the company, we can use the information provided. The mean volume of juice in a random sample of bottles is x¯ = 27 ounces, with a margin of error of 4 ounces.
A confidence interval is a range of values within which we can be confident that the true population parameter (in this case, the mean number of ounces of juice) falls.
To construct the confidence interval, we need to determine the level of confidence. Let's say we want a 95% confidence level, which is a common choice. This means that we want to be 95% confident that the true mean number of ounces of juice falls within the interval.
To calculate the confidence interval, we need to consider the margin of error and the sample mean. The margin of error represents the maximum likely difference between the sample mean and the true population mean.
To construct the confidence interval, we add and subtract the margin of error from the sample mean:
Lower bound = x¯ - margin of error
Upper bound = x¯ + margin of error
Substituting the values given:
Lower bound = 27 - 4 = 23 ounces
Upper bound = 27 + 4 = 31 ounces
Therefore, the confidence interval for the mean number of ounces of juice bottled by the company is 23 to 31 ounces. This means that we can be 95% confident that the true mean number of ounces of juice falls within this range.