Question: A sample of 16 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was 2 ounces with a standard deviation of 0.12 ounces. The population standard deviation is known to be 0.1 ounce.
a. Define the Random Variable X, in words.
b. Which distribution should you use for this problem? Explain your choice.
c. Construct a 90% confidence interval for the population average weight of the candies.
d. State the confidence interval in words.
e. Calculate the error bound (EBM).
f. Construct a 98% confidence interval for the population average weight of the candies.
g. State the confidence interval in words.
h. Calculate the error bound (EBM).
g. In complete sentences, explain why the confidence interval in (f) is larger than the confidence interval in (c).