Question

The weights of a random sample of cereal boxes that are supposed to weigh 1 pound are given below. Estimate the standard deviation of the entire population with 80% confidence. 1.03 0.97 1.02 1.01 0.99 0.96 1.01 1.05 Confidence interval for o:

Answer 1

The estimated standard deviation of the entire population with 80% confidence is approximately 0.032 pounds.

Explanation:

To estimate the standard deviation with 80% confidence, we use the formula for the margin of error in a confidence interval for the standard deviation. Using the given sample data, we calculate the standard deviation of the sample, which is 0.035 pounds. Next, we determine the margin of error using the critical value corresponding to an 80% confidence level and the sample size.

Finally, we subtract and add the margin of error from the sample standard deviation to obtain the confidence interval for the population standard deviation. The estimated standard deviation of the entire population is then the average of these upper and lower bounds, resulting in an approximate value of 0.032 pounds.