04 Jun Question UNIVERSITY OF CALGARY Department of Mathematics and Statistics STAT 213-L01 Sample Midterm Exam 2 Winter 2015
Question
UNIVERSITY OF CALGARY
Department of Mathematics and Statistics
STAT 213-L01 Sample Midterm Exam 2 Winter 2015
First Name: Last Name:
1 (MANUAL). A candy company fills 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 find 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% confidence interval to estimate the mean number of pieces per package for
the population. Interpret the confidence interval.
1
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% confidence interval for the population average amount
of purchases. Justify the confidence interval estimate you used.
2
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% confidence interval to
estimate the population proportion of commercial airline pilots who are more than 40 years of
age. Interpret the confidence interval.
(b) In order to estimate the true proportion of pilots of more than 40 years of age with a
confidence level of 95% and a margin of error of 5%, what minimum sample size should we
obtain?
3
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
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