Econ 2500 Section E 3.0 - Fall 2015 Assignment 1 | Complete Solution

Econ 2500 Section E 3.0 - Fall 2015
Assignment 1

Question 1: At the PISA Web site (www.pisa.oecd.org), there are summary statistics for
math scores of 15-year-old males and females for various countries separately. The mean
math scores for males, the mean math scores for females, and also the di erence of the two
means are listed in the Excel le.

a. Use any software and obtain the histogram for the mean math scores for males.
b. How would you describe the overall shape of this data set? Do you suspect any outlying
group in this data set?
c. Report the 5-number summaries for the di erence of the two means. (Note: Don't use
software. Use the method discussed in class).
d. Obtain the back-to-back stemplot and compare the distribution of the mean math
scores for males and for females.
e. Use any software and report the sample mean and sample standard deviation for the
mean math scores for females.
f. Based on the given data, what proportion of the mean math scores for females falls
within 2 standard deviation of the mean?
Question 2: It is well-known that the relationship between degree Fahrenheit (F) and
degree Celsius (C) is
F =
9
5
C + 32
We randomly selected 100 days in October from 2010-2014 and recorded the temperature
(in degree Fahrenheit) of New York City. We have the following summary statistics from R:
Min. 1st Qu. Median Mean 3rd Qu. Max. std dev
66.00 73.00 76.50 76.55 79.00 92.00 5.015884
Report the summary statistics in degree Celsisus.

Question 3: The amount of sodium is recorded for each of the 200 randomly selected
9-ounce serving of chicken noodle soup which yields a mean of 1100 mg and a standard
deviation of 150 mg. Moreover, the data distribution looks approximately bell-shaped.
a. Approximatelhy, what proportion of soups have amount of sodium is less than 950 mg?
b. Approximatelhy, what proportion of soups have amount of sodium is between 800 mg
and 1550 mg?

c. An expert said that when the amount of sodium is 6 standard deviation higher than
the mean, it is then considered to be dangerous. In this case, what amount (in mg) is
considered to be dangerous?
Question 4: Consider the follow split stem-and-leaf plot of 52 data points:
Leaf unit = 0.1
1 12
1 668
2 04
2 888
3 1334
3 555778899
4 0000111233444
4 56788
5 222
5 779
6 03
6 6
7 2
7
8
8 9
R gives the following summary statistic:
Min. 1st Qu. Median Mean 3rd Qu. Max.
1.100 3.375 4.000 4.060 4.725 8.900
Also the sample variance is reported to be 2.1570.
a. What percentage of data falls below 3.0?
b. Based on the R output, identify all outliers and extreme outliers?
c. Is Empirical Rule applicable here? Why or why not?
d. What do the Empirical Rule and Chebyshev Rule said about the percentage of data
fall within 2 standard deviation of the mean? How about the actual percentage of data
fall within that range?
e. Find the z-score for the largest and smallest data points.

Question 5: Many people grab a granola bar for breakfast or for a snack to make it
through the afternoon slump at work. For the Kashi GoLean Crisp Chocolate Caramel 45
grams bar, the company claimed that the mean amount of protein in each bar is 9 grams with
a standard deviation of 1.5 gram. Suppose the distribution of protein in a bar is normally
distributed.

a. What is the probability that the amount of protein is less than 7.75 grams?
b. What is the probability that the amount of protein is between 7.8 and 8.2 grams?
c. Suppose the amount of protein is at least 8.1 grams. What is the probability that it is
more than 8.3 grams?
d. What is the amount of protein that is exceeded by 2.5% of all the bars?

Question 6: The types of books borrowed by 36 randomly selected students from York
University are:
Psychology Science Education Education Technology Science
Law Technology Science Education Law Technology
Psychology Literature Literature Education Psychology Law
Psychology Literature Technology Law Psychology Literature
Technology Literature Science Education Technology Science
Literature Psychology Law Education Law Education
a. Obtain a bar chart using relative frequency on the vertical axis.
b. Obtain a pie chart for this data set.
c. Do you think the York University should try to acquire more books in one particular
subject area? Why or why not?

Question 7: Three of the following students will form the Executive Committee for the
York University Students Council:
Annie Charles Darwin Ellen Ginny Justin Kerri Mandy Steve Zach
It was decided that the following random digits will be used to help to choose the committee.
09297 00412 71238 60500 14873 07095 08709
Clearly explain who will be on the committee.