STAT213 L01 Sample Midterm Exam 2 Complete Solution

Question: #1642

UNIVERSITY OF CALGARY
Department of Mathematics and Statistics

First Name: Last Name:
UC ID:
No cellphones. No internet except http://people.ucalgary.ca/sunb/. Only the
exam papers, Minitab, pencils/pens, and a simple calculator are allowed.

1 (MANUAL). A candy company lls a 550-g package of Halloween candy with individually wrapped pieces of candy. The number of pieces of candy per package varies because the package is sold by mass. The company wants to estimate the average number of pieces per package. Inspectors randomly sample 120 packages of this candy and count the number of pieces in each package. They nd that the sample mean number of pieces is 18.72. Assuming a population standard deviation of 0.8735.

(a) What is the point estimate of the average number of pieces per package?

(b) Construct a 99% con dence interval to estimate the mean number of pieces per package for the population. Interpret the con dence interval.

2 (MINITAB). A researcher is interested in estimating the average purchase amount for convenience stores in Canmore, Alberta. To do so, she randomly sampled 24 purchases from several convenience stores in Canmore and tabulated the amounts to the nearest dollar. The sample data are given below.
2 11 8 7 9 3 5 4 4 8 10 8
7 6 6 7 3 2 4 2 3 6 8 4
Use the sample data and construct a 90% con dence interval for the population average amount of purchases. Justify the con dence interval estimate you used.

3 (MANUAL). What proportion of commercial airline pilots are more than 40 years of age? Suppose a researcher has access to a list of all pilots who are members of the Air Line Pilots Association. If this list is used as a frame for the study, she can randomly select a sample of pilots, contact them, and ascertain their ages. From 89 of these pilots so selected, she learned that 48 are more than 40 years of age.

(a) Use two decimals for your sample proportion. Construct a 96% con dence interval to estimate the population proportion of commercial airline pilots who are more than 40 years of age. Interpret the con dence interval.

(b) In order to estimate the true proportion of pilots of more than 40 years of age with a con dence level of 95% and a margin of error of 5%, what minimum sample size should we obtain?

4 (MANUAL). Statistics Canada reports that the average annual consumption of fresh fruit per person in the year 2013 is 39.4 kg. Suppose the standard deviation of fresh fruit consumption is about 12 kg. A researcher took a random sample of 40 people in 2014 and had them keep a record of the fresh fruit they ate for one year. Suppose the sample average consumption of fresh fruit per person is 41 kg. Test at the signi cance level of 0.05 whether the average annual consumption of fresh fruit per person in Canada has increased.

Solution: #1627

STAT213-L01 Sample Midterm Exam 2 Complete Solution

The point estimate of the average number of pieces per package is the sample average which is 18.72.The population standard devi...