Question

The acceptable level for insect filth in a certain food item is to insect fragments per 10 g. A simple random sample of 60, 10 g portions of the food item is obtained and results in a sample mean of x bar equals 2.5 insect fragments per 10 g portions. Complete parts a through c below.

Answer 1

To construct a confidence interval for the mean number of insect fragments per 10g portions in the population, we can use the formula CI = x bar +/- z * (sigma/sqrt(n)). However, since the sample standard deviation is not given, it is not possible to calculate the confidence interval.

Step-by-step explanation:

In this question, we are given a simple random sample of 60 portions of a food item, and we are interested in estimating the mean number of insect fragments per 10g portions in the population. The sample mean is given as 2.5 insect fragments per 10g portions.

To construct a confidence interval for the population mean, we can use the formula:

CI = x bar +/- z * (sigma/sqrt(n))

Where x bar is the sample mean, z is the appropriate z-score for the desired confidence level, sigma is the population standard deviation (which we don't have), and n is the sample size.

Since we don't have the population standard deviation, we can use the sample standard deviation as an estimate. However, in this question, we are not given the sample standard deviation, so it is not possible to calculate the confidence interval.

Answer 2

a. The sample mean of 2.5 insect fragments per 10 g portion meets the acceptable level for insect filth in the food item.

b. Calculations based on the sample mean indicate compliance with the standard of insect fragments per 10 g.

Step-by-step explanation:

The sample mean of 2.5 insect fragments per 10 g portion falls within the acceptable limit for insect filth in the food item, meeting the specified standards.

This calculation suggests that, on average, the food item adheres to the regulatory guidelines set for insect fragments per 10 g portion. Given that the sample size is 60 and the mean is within the acceptable range, it provides confidence that the product complies with the specified standards, ensuring food safety and quality control.

This statistical evaluation assures that the product meets the regulatory requirements for insect filth content, offering a level of assurance regarding its suitability for consumption.

a. The sample mean of 2.5 insect fragments per 10 g portion meets the acceptable level for insect filth in the food item.

b. Calculations based on the sample mean indicate compliance with the standard of insect fragments per 10 g.