A sample of fifteen 2-liter bottles of a soft drink delivers a mean weight of 2009 milliliters with a sample standard deviation of 11 milliliters. The quality assurance department wants to determine if there is a true fill problem, so they determine the confidence interval at 95% confidence to be ________.

Question

A sample of fifteen 2-liter bottles of a soft drink delivers a mean weight of 2009 milliliters with a sample standard deviation of 11 milliliters. The quality assurance department wants to determine if there is a true fill problem, so they determine the confidence interval at 95% confidence to be ________.

Answer 1

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (±.025) and its Z score. Insert Z score and other data into equation below.

95% = mean ± Z(SD)

Answer 2

Indicate your specific subject in the "School Subject" box, so those with expertise in the area will respond to the question. (You lucked out.)

Answer 3

To determine the confidence interval for the mean weight of the 2-liter bottles of soft drink, we can use the formula:

Confidence Interval = mean ± (critical value * standard error)

First, calculate the critical value. Since we want a 95% confidence interval, we need to find the critical value corresponding to an alpha level (α) of 0.05. This critical value will be used to account for the variability in the sample mean.

Since we have a sample size of fifteen (n = 15), we need to calculate the degrees of freedom (df), which is equal to n - 1. In this case, df = 15 - 1 = 14.

To find the critical value, we need to use a t-distribution table or a calculator. The critical value for a 95% confidence interval with df = 14 is approximately 2.1448.

Next, calculate the standard error. The standard error is a measure of the variability of the sample mean and is calculated as the sample standard deviation divided by the square root of the sample size:

Standard Error = sample standard deviation / √sample size

In this case, the sample standard deviation is 11 milliliters and the sample size is 15:

Standard Error = 11 / √15 ≈ 2.839 milliliters

Now we have all the values we need to calculate the confidence interval:

Confidence Interval = mean ± (critical value * standard error)
Confidence Interval = 2009 ± (2.1448 * 2.839)

Calculating:

Confidence Interval = 2009 ± 6.08

Thus, the 95% confidence interval for the mean weight of the 2-liter bottles of soft drink is approximately (2002.92, 2015.08).