Homework #2 9/14/15

READING 2.1 PROBLEMS #7-15 ODDS

1. Which country had the most Internet users in 2010?

• China, with over 400,000,000

2. Approximately how many Internet users did the United Kingdom have in 2010?

• About 50,000,000

3. Approximately how many more users were in China than in Germany in 2010?

• 350,000,000

1. What percent of the respondents believe divorce is morally acceptable?

• Approximately 69%

2. If there were 240 million adult Americans in 2010, how many believe that divorce is morally wrong?

• Approximately 52.8 million

3. If Gallup claimed that the results of the survey indicate that 8% of Americans believe that divorce is acceptable in certain situations, would you say this statement is descriptive or inferential? Why?

• This is an inferential statement because his data only speaks to the exclusive sample of people that he questioned; in order to make an accurate statement about th entire population, you would need to ask everyone. Because that is not possible, he is making an inference based off of his sample results about the population.

1. What proportion of 18-to-34-year-old respondents are more likely to buy when made in America? What proportion of 35-to-44-year-old respondents are more likely to buy when made in America?

• About 0.425 of 18-34 year-olds and about 0.610 of 35-44 year-olds are more likely to buy when made in America.

2. Which age group has the greatest proportion who are more likely to buy when made in America?

• 55+

3. Which age group has a majority of respondents who are less likely to buy when made in America?

• 18-34

4. What is the apparent association between age and likelihood to buy when made in America?

• Younger age groups are less likely to buy something made in America, while older age groups are more likely to buy things made in America, and have less people who would be less likely as well.

1. Construct a relative frequency distribution.

Never……………125…….0.26

Rarely……………324…….0.68

Sometimes……….552…….0.12

Most of the time…1257……0.26

Always…………..2518……0.53

2. What percentage of respondents answered “always”?

• 52%

3. What percentage of respondents answered “never” or “rarely”?

• 9%

4. Construct a frequency bar graph.

x<-c(125,324,552,1257,2518)
y<-c("Never", "Rarely", "Sometimes", "Most", "Always")
barplot(x,main = "Frequency",names.arg = y, col = c("light blue","dark blue"))

5. Construct a relative frequency bar graph.

z<-c(0.26,0.68,0.12,0.26,0.53)
w<-c("Never","Rarely","Sometimes","Most","Always")
barplot(z,main = "Relative Frequency",names.arg = w, col = c("light blue","pink","light green","gold","darksalmon"))

6. Construct a pie chart.

pie(x,labels = y, main = "Frequency Pie Chart")

7. Suppose that a representative from the Centers for Disease Control says, “52.7% of all college students always wear a seat belt.” Is this a descriptive or inferential statement?

• This statement is inferential because not every college student in the population was involved in the survey, and they are making a statement about the entire population of college students based on the results from their sample. By assuming conclusions, they are making an inference.

1. Construct a relative frequency distribution.

More than 1 hour/day……377……0.37

Up to 1 hour/day…………192…..0.19

A few times/week………..132…..0.13

A few times/month……….81……0.08

Never……………………..243…..0.24

2. What proportion of those surveyed never use the internet?

• 23%

3. Construct a frequency bar graph.

a<-c(377,192,132,81,243)
b<-c("Hour+","Hour","Weekly","Monthly","Never")
barplot(a, main = "Frequency Graph",names.arg = b,col = c("Light green","dark green"))

4. Construct a relative frequency bar graph.

g<-c(0.37,0.19,0.13,0.08,0.24)
h<-c("Hour+","Hour","Weekly","Monthly","Never")
barplot(g, main = "Relative Frequency Graph",names.arg = h, col = c("powderblue","lavenderblush3","plum2","deepskyblue","lavender"))

5. Construct a pie chart.

pie(a, labels = y, main = "Frequency", col = c("ghostwhite","floralwhite","aliceblue","lavenderblush","lavender"))

6. A local news broadcast reported that 37% of adult Americans use the Internet more than 1 hour a day. What is wrong with this statement?

• They did not give evidence as to how that percentage was acquired.

READING 2.2 PROBLEMS 9-14

1. What was the most frequent outcome of the experiment?

• Rolling an 8

2. What was the least frequent?

• Rolling a 2

3. How many times did we observe a 7?

• A 7 was rolled 15 times

4. How many more 5’s were observed than 4’s?

• 4 more 5’s than 4’s

5. Determine the percentage of time a 7 was observed.

• 15%

6. Describe the shape of distribution.

• The distribution is skewed left because the tail to the left of the peak is longer than the tail to the right of the peak.

1. What is the most frequent number of cars sold in a week?

• 4 cars

2. For how many weeks were two cars sold?

• 9 weeks

3. Determine the percentage of time two cars were sold.

• 128%

4. Describe the shape of distribution.

• The distribution is skewed right because the tail to the right of the peak is longer than the tail to the left.

1. How many students were sampled?

• 200

2. Determine the class width.

• The class width is 9.9

3. Identify the classes and their frequencies

60-69……2 70-79……3 80-89……13 90-99……42 100-109….58 110-119….40 120-129….31 130-139….8 140-149….2 150-159….1

4. Which class has the highest frequency?

• 100-109

5. Which class has the lowest frequency?

• 150-159

6. What percent of students had an IQ of at least 130?

• 5.5%

7. Did any students have an IQ of 165?

• No

1. Determine the class width

• 319.8

2. Identify the classes

0-199 200-399 400-599 1000-1199 1400-1599

3. Which class has the highest frequency?

• 0-199

4. Describe the shape of the distribution.

• The distribution is skewed right because the tail to the right of the peak is longest.

5. A reporter writes the following statement: “According to the data, Texas had 1463 alcohal-related deaths, while Vermont had only 15. So the roads in Vermont are much safer.” Explain what is wrong with this statement and how a fair comparison can be made between alcohal related traffic fatalities in Texas versus Vermont.

• This statement does not account for any other safety variables that determine the safety of a road, just the alcohal casualties. Also, there may be reasons why Texas had a peak in alcohal casualties that year which the reporter does not mention or account for. Instead, he could’ve said, “According to the National Highway Traffic Administration, Texas had a much greater number of fatalities related to alcohal in 2008.”

1. Annual household incomes in the US:

• Bell-shaped.I think that the incomes would have an average in the middle, but that people would tail out on the left and right who made less-than-average income and greater incomes.

2. Scores on a standardized test exam such as the SAT:

• Skewed right. I think that a smaller number of people would score low, majority would score in the low-middle range, and then the smaller majority would get high scores since it is a difficult exam being taken by the masses. The shape described would have a long tail to the right of the peak.

3. Number of people living in a household:

• Skewed right. I think that most people would have lower numbers with a small tail of people who have more people living with them.

4. Ages of patients diagnosed with Alzheimer’s Disease:

• Skewed left. Most likely, the older age range to the right would hold the majority, with a younger age range having few cases making up the small tail to the left of the peak.

1. Number of alcohalic drinks consumed per week:

• Bell shaped. I would expect the average amounts of drinks consumed to be in the middle with the majority, and have more drinks or less drinks tailing out of the sides.

2. Ages of students in a public school district:

• Uniform. There would most likely be just as many younger children as older children within a school district.

3. Ages of hearing-aid patients:

• Skewed left. The older age group to the right side would most likely be the peak, with the younger age groups tailing out to the left.

4. Heights of full-grown men:

• Bell shaped. The majority of heights would likely be average and in the middle, while the taller and shorter would likely take up equal space on the left and right sides.

hist(x=iris$Sepal.Length, col = c("palevioletred","violet"))

• The shape of this is Bell-shaped because it is nearly symmetric on both sides of the peak.