Two competing ski slopes in Colorado advertise their powder base each day in an effort to attract more skiers. A random sample of the powder base depth (in inches) was obtained for each ski resort on days during a recent winter. Assume
a. Find a 99% confidence interval for the true mean powder depth at Breckenridge Ski Resort.
b. Find a 99% confidence interval for the true mean powder depth at Vail Ski Resort.
c. Use the results in parts (a) and (b) to determine whether there is any evidence to suggest a difference in the true mean powder depths at these two ski resorts. d. What assumptions were necessary to construct the confidence intervals in parts (a) and (b)?
The nutritional value of every food product sold in the United States is listed on the package in terms of protein, fat, etc. A researcher randomly selected 50 one-ounce samples of various nuts and carefully measured the amount of protein (in grams) in each sample. The sample mean amount of protein and the assumed standard deviation for each type of nut are given in the table below.
a. Find a 95% confidence interval for the true mean amount of protein in each type of nut. Based on these intervals, is there any evidence to suggest that the mean amount of protein is different for cashews and pecans? How about filberts and pecans?
b. Answer part (a) using a sample size for each nut of 18.
Snail farming, or heliciculture, has become more popular and lucrative in many parts of the world. In April 2013, John Morton, head of U.S. Immigration and Customs Enforcement, resigned with plans to open a snail farm.The Helix pomatia, or escargot snail, grows to full size in 2 to 3 years and weighs 15 to 25 grams. A random sample of snails of this type was obtained from a farm near the town of Targovishte, Bulgaria. Each snail was carefully weighed (in ounces). Assume
a. Find a 99% confidence interval for the true mean weight of these snails.
b. Using your answer in part (a), is there is any evidence to suggest that the population mean weight is more than 20 grams?
c. How large a sample size is necessary for the bound on the error of estimation to be 0.5 gram?