Hi there,

1) (A) Classify the following as an example of nominal, ordinal, interval, or ratio level of measurement, and state why it represents this level: zip codes for the state of Pennsylvania

Nominal -- there is no ordering to the numbers -- meaning no one zip code is "better" than another because it has a different number

(B) Determine if this data is qualitative or quantitative: Nationality

Qualitative -- it is not numerical

(C) In your own line of work, give one example of a discrete and one example of a continuous random variable, and describe why each is continuous or discrete.
Discrete -- the number of people in my office -- this is a whole number

Continuous -- the temperature in my office -- this doesn't have to be a whole number, or even a fraction -- it can be any value

2) A newsmagazine asks 1200 students what college they attend, and how many times per week they attend a party where alcohol is served. The news magazine determines the mean number of parties per week for each school, and publishes a ranking of the nation's top ten party schools.
I. What is the population?

All college students

II. What is the sample?

The 1200 students who were surveyed

III. Is the study observational or experimental? Justify your answer.

This is observational, since they are asking people what they do, as opposed to telling them how to behave

IV. What are the variables?

the college they attend

how many times per week they go to a party with alcohol

V. For each of those variables, what level of measurement (nominal, ordinal, interval, or ratio) was used to obtain data from these variables?

the college is nominal, since it's not even numerical

the number of times per week is ratio, since it has a real meaning, and if you go to 6 parties, that's twice as many as 3 parties

3) Construct both an ungrouped and a grouped frequency distribution for the data given below:
146 150 149 153 160 149 146 147 146 158
149 155 146 158 146 148 152 152 148 160

ungrouped:

grouped:

4) Given the following frequency distribution, find the mean, variance, and standard deviation. Please show all of your work.
Class Frequency
71-73 23
74-76 12
77-79 7
80-82 25
83-85 21

mean =

sum(x*n(x))/total

using the midpoints of the intervals

= (72*23+75*12+78*7+81*25+84*21)/(23+12+7+25+21)

= 78.3068

var

= sum(x^2*n(x))/total - mean^2

= (72^2*23+75^2*12+78^2*7+81^2*25+84^2*21)/(23+12+7+25+21) - 78.3068^2

= 21.6928

stdev = sqrt(var)

= sqrt(21.6928)

= 4.65755

5) The following data lists the average monthly snowfall for January in 15 cities around the US:

25 19 21 14 24 30 28 33
32 44 25 43 5 20 42

Find the mean, variance, and standard deviation. Please show all of your work.
mean = average

= (25+19+21+14+24+30+28+33+32+44+25+43+5+20+42)/15

= 27

var = sum of square deviations / (count-1) for the sample variance

= ((25-27)^2+(19-27)^2+(21-27)^2+(14-27)^2+(24-27)^2+(30-27)^2+(28-27)^2+(33-27)^2+(32-27)^2+(44-27)^2+(25-27)^2+(43-27)^2+(5-27)^2+(20-27)^2+(42-27)^2)/14

= 118.57

stdev = sqrt(var)

10.889

6) Rank the following data in increasing order and find the positions and values of both the 15th percentile and 84th
percentile. Please show all of your work.
4 5 4 5 8 0 6 5 9 2 1 9
sorted

15th percentile is between the 2nd and 3rd: 1.5

84th percentile is between the 10th and 11th: 8.5


7) For the table that follows, answer the following questions:
x y
1 3
2 7
3 11
4


- Would the correlation between x and y in the table above be positive or negative?
Positive
- Find the missing value of y in the table.
11+4 = 15
- How would the values of this table be interpreted in terms of linear regression?
These are data points that all fit exactly on a line, so the regression would give the exact line through the points
- If a "line of best fit" is placed among these points plotted on a coordinate system, would the slope of this line be positive or negative?

It's positive, since the correlation is positive

Let me know if you have any questions,

Scott