Question: You work for a company that prepares and distributes frozen foods. The package claims a net weight of 14.5 ounces. A random sample of today's production was weighed, producing the following data set:
14.43, 14.37, 14.38, 14.29, 14.60, 14.45, 14.16, 14.52, 14.19, 14.04, 14.31
A sample was also selected from yesterday's production. The average was 14.46 and the standard deviation was 0.31.
a. Estimate the mean weight you would have found had you been able to weigh all packages produced today.
b. For a typical individual package produced yesterday, approximately how different was the actual weight from yesterday's average?
c. Find the 95% confidence interval for the mean weight for all packages produced today.
d. Identify the hypotheses you would work with to test whether or not your claimed weight is correct, on average, today.
e. Is there a significant difference between claimed and actual mean weight today? Justify your answer.