Statistics 226
Supplemental Instruction
Iowa State University / Leader: / Luyun
Course: / Stat 226
Instructor: / Anna Peterson
Date: / 3/9/16
CI interpretation: it is known that the standard deviation in the volumes of 24-ounce (710ML) bottles of natural spring water bottled by a particular company is 6 Ml. Ninety bottles are randomly sampled and measured and yielded a mean volume of 708 ML.
(a) Find a 98% confidence interval for the true mean volume of all bottles of natural spring water.
(b) What Z* value was used to create this confidence interval?
(c) We want a more precise estimate of the true mean volume and changing the population standard deviation is not an option. What can we do to get a more precise estimate?
(d) If we decrease the level of confidence holding all else constant, would the interval get wider or narrower?
(e) Based on the above results, do you believe the bottling process is on target (710 ml) Explain why or why not.
(f) We now randomly sample just 50 bottles and wish to calculate a 98% confidence interval for the true mean volume of the bottles. We expect to have more/less precision (circle one). That is, our confidence interval will be: narrower/wider than in question 1 (circle one).
(g) The description of the problem did not make any statement about the distribution of the bottle volumes? Why or why not?
City Parking. Hoping to lure more shoppers downtown. A city built a new public parking garage in the central business district. The city plans to pay for the structure through parking fees. During a two-month period (a total of 61 days) the mean of the daily fees collected was $1,535. From similar projects, the population standard deviation is known to be $190.
(a) In the context of this problem, what does μ represent?
(b) Calculate a 90% confidence interval for the unknown population mean μ, show all your work.
(c) Give the interpretation of the confidence interval that you calculated in part (b).
(d) Calculate a 95% confidence interval for the unknown population mean μ, show all your work.
(e) The consultant who advised the city on this project predicted that parking revenue would average $1590 per day. On the basis of your confidence interval, do you think the consultant’s prediction is reasonable? Explain why or why not.
(f) Suppose that the parking fee data do not exactly follow a Normal distribution, but they are not terribly skewed either. Are the results in (b) through (d) still valid? Explain your response.