Exam 1 Review
Has the percentage of young girls drinking milk changed over time? The following table is consistent with the results from “Beverage Choices of Young Females: Changes and Impact on Nutrient Intakes” (Shanthy A. Bowman, Journal of the American Dietetic Association, 102 (9), pp. 1234 – 1239:
Nationwide Food Survey Years
1987 - 1988 1989 - 1991 1994 - 1996 Total Drinks Fluid Milk Yes 354 502 366 1222 No 226 335 366 927 Total 580 837 732 2149
1. Find the following a. What percent of young girls reported that they drink milk? (1222 ÷ 2149)100 = 56.86%
b. What percent of the young girls were in the 1989 – 1991 survey? (837 ÷ 2149)100 = 38.94%
c. What percent of the young girls who reported that they drink milk were in the 1989 – 1991 survey? (502 ÷ 1222)100 = 41.08%
d. What percent of the young girls in the 1989 – 1991 reported that they drink milk? (502 ÷ 837)100 = 59.97%
2. What is the marginal distribution of milk consumption? Yes: (1222 ÷ 2149)100 = 56.86% No: (927 ÷ 2149)100 = 43.13%
3. Do you think that milk consumption by young girls is independent of the nationwide survey year? Use statistics to justify your reasoning.
Of all young girls surveyed, 56.9% reported drinking milk, but 60% of the young girls reported drinking milk in the 1989-1991 survey. Since these percentages differ, milk consumption and year are not independent. 4. Sketch a stem and leaf for this data: 49, 67, 38, 55, 62, 54, 36, 41, 56, 43, 49, 75, 44, 60, 48, 52, 48, 53, 59, 32.
Firs put them in ascending order: 32 36 38 41 43 44 48 48 49 49 52 53 54 55 56 59 60 62 67 75
7 5 6 0 2 7 5 2 3 4 5 6 9 4 1 3 4 8 8 9 9 3 2 6 8
5. One of the reasons that the Monitoring the Future (MTF) project was started was “to study the changes in the beliefs, attitudes, and behavior of young people in the United States.” Data are collected from 8th, 10th, and 12th graders each year. To get a representative nationwide sample, surveys are given to a randomly selected group of students. In Spring 2004, students were asked about alcohol, illegal drug, and cigarette use. Describe the W’s. If the information is not given, state that it is not specified. Who: 8th, 10th, and 12th graders (all categorical variables)
What: alcohol, illegal drug, and cigarette use
When: Spring 2004
Where: United States
How: Survey
Why: “to study changes in the beliefs, attitudes, and behavior of young people in the United States.”
6. The students in a biology class kept a record of the height (in centimeters) of plants for a class experiments: 49, 67, 38, 55, 62, 54, 36, 41, 56, 43, 48, 75, 44, 60, 48, 52, 48, 53, 59, 32. Find the:
32 36 38 41 43 44 48 48 48 49 52 53 54 55 56 59 60 62 67 75
a) mean : (32 + 36 +…+ 75) ÷ 20 = 1020 ÷ 20 =51
b) median : (49 + 52) ÷ 2 = 50.5
c) Q1: (43 +44) ÷ 2 = 43.5 d) Q3: (56 +59) ÷2 = 57.5
e) IQR: 57.5 – 43.5 = 14
f) Range: 75 – 32 = 43
g) Standard deviation: 32 36 38 41 43 44 48 48 48 49 52 53 54 55 56 59 60 62 67 75
Y Values Deviations (y – Ў) Squared Deviations 32 32 – 51 = -19 361 36 36 – 51 = -15 225 38 -13 169 41 -10 100 43 -8 64 44 -7 49 48 -3 9 48 -3 9 48 -3 9 49 -2 4 52 1 1 53 2 4 54 3 9 55 4 16 56 5 25 59 8 64 60 9 81 62 11 121 67 16 256 75 24 576
S2 = (361 + 225 + …+ 576) ÷ (20 – 1) =113.263
S = √113.263 = 10.64 7. Here is a histogram displaying the amount of time watching television a week for a group of college students. Describe the time distribution. Make sure to comment on the shape, center, and spread.
The histogram of amount of time spent watching TV is unimodal and skewed to the right. The median time spent watching TV is around 8 hours. The data is very spread with people reporting watching TV between 0 and 30 hours with two outliers around 40 and 60.
8. This box plot displays the amount of time college students spend studying (in hours) a week. Write a few sentences describing the amount of study time for both males and females.
The median time spent studying for males and females are about the same, between 7 and 8 hours. Females have a larger range of time spent studying; 28 compared to 18. There is one outlier at 40 hours for males. The distribution for males appears to be symmetric where the distribution for females is skewed to the right. 9. Using the table below create a bar chart.
Goals of Thrasher Hockey Players
Player Goals Ilya Kovalchuk 20 Todd White 14 Vyacheslav Kozlov 16 Bryan Little 21 Colby Armstrong 13
Goals
25
20
15
10
5
0 Kovalchuk White Kozlov Little Armstrong 10. Create a pie chart using the table below.
The percentage of high school students who drank alcohol (more than a few sips) for the first time before the age of 13; the frequency of having had their first drink before 13 is (according to the 2005 Youth Risk Behavior Surveillance Survey (YRBSS) conducted by the Centers for Disease Control and Prevention):
Grade Percentage 12th 19.3 11th 20.5 10th 26.2 9th 33.9
Percentage of students who drank before age 13
19%
34% 12th 11th 10th 9th
21%
26% 11. The data below show the number of shoplifters caught at Lenox mall each week for 6 months. Create a dotplot of these data
2 5 0 1 4 3 2 3 6 2 1 3 3 5 5 4 4 3 5 4
0 1 2 3 4 5 6