Question

A technician working for the Chase-National Food Additive Company would like to estimate the preserving ability of a new additive. This additive will be used for Auntie’s brand preserves. Based on past tests, it is believed that the time to spoilage for this additive has a standard deviation of 5 days. To be 99% confident of the true mean time to spoilage, what sample size will be needed to estimate the mean time to spoilage with an accuracy of one day?

Answer 1

To estimate the mean time to spoilage with an accuracy of one day and 99% confidence, a sample size of at least 133 is needed.

Step-by-step explanation:

To estimate the mean time to spoilage with an accuracy of one day and be 99% confident, we need to calculate the required sample size. Since the standard deviation is known (5 days) and the desired level of confidence is 99%, we can use the formula:

Sample Size = (Z-score * Standard Deviation / Desired Accuracy) ^ 2

Plugging in the values, we get:

Sample Size = (2.576 * 5 / 1) ^ 2 = 132.62

Therefore, we would need a sample size of at least 133 to estimate the mean time to spoilage with an accuracy of one day and a 99% confidence level.