Question

The historical data of Velvetta Inc., a healthcare products manufacturer, have shown that in a production process for filling bottles of shampoo, variance in the volume is constant; however, clogs in the filling machine often affect the average volume. The historical standard deviation is 5 milliliters. In filling 250-milliliter bottles, a sample of 20 found an average volume of 242 milliliters.

Velvetta Inc. Shampoo Production
Alpha Value 0.05
Standard Deviation 5
Sample Size 20
Sample Average 242

Based on the data above, calculate the margin of error for a 95% confidence interval.Please show the work and explain why

Answer 1

The margin of error for a 95% confidence interval is 1.382.

Step-by-step explanation:

To calculate the margin of error for a 95% confidence interval, we can use the formula: margin of error = critical value * standard deviation / square root of sample size. The critical value for a 95% confidence interval is 1.96 (which corresponds to a two-tailed test). Plugging in the values from the problem, we have: margin of error = 1.96 * 5 / sqrt(20) = 1.382