\({\bf (1)}\) Define the following terms: * (a) Population * (b) Sample * (c) Parameter * (d) Statistic

\({\bf (2)}\) Explain the difference between a qualitative (categorical) and a quantitative variable

\({\bf (3)}\) Explain the difference between a discrete and a continuous variable and give an example of each

\({\bf (4)}\) Explain the difference between a nominal and an ordinal variable and give an example of each

\({\bf (5)}\) At What age did women marry? A historian wants to estimate the average age at marriage of women in New England in the early 19th century. Within her state archives, she finds marriage records for the years \(1800 - 1820\), which she treats as a sample of all marriage records from the early 19th century. The average age of the women in the records is \(24.1\) years of age. Using the appropriate statistical method, she estimates that the average age of brides in the early \(19^{th}\)- century New England was between \(23.5\) and \(24.7\) years of age.

\({\bf (6)}\) Consider the following data obtained from flipping a coin 15 times. A value of \(H\) denotes the coin was heads whereas a value of \(T\) denotes the coin flip was tails.
coin.flip.result. H H H T H T T T H H T T T H T

Compute the frequency table for the variable ``coin flip result” and answer the following questions:

Result Frequency Relative Frequency
H
T

\({\bf (7)}\) A survey about color preferences reported the age distribution of the people who responded. Below are the results
1 Age Group (Years) 1-18 19-24 25-35 36-60 51-69 70 and over
2 Counts 10 97 70 36 14 5

Use this table to answer parts a - d

\({\bf (8)}\) Email spam is the curse of the internet. The table below gives a compilation of the most common types of spam
Type of Spam Percentage
Adult 14.5
Financial 16.2
Health 7.3
Leisure 7.8
Products 21.0
Scams 14.2

Use the table to answer the questions a and b

\({\bf (9)}\) A farmer in Idaho is interested in the number of rainy days in a given year so he records the number of rainy \(R\), cloudy \(C\) and sunny \(S\) days over two weeks in \(May\). His observations are \[\{R,R,C,C,C,S,S,C,R,R,C,R,S,S\}\]. Use the farmers observations to answer the following questions.

\({\bf (10)}\) Consider the following data from a survey conducted on college students in the state of Florida. As part of their research, surveyors recorded the high school performance (measured in grade point average - GPA) of 35 college students from across the state. For your convenience the data have been sorted from least to greatest:

\[2.0, 2.1, 2.3, 2.8, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0,\] \[3.0, 3.0, 3.0, 3.1, 3.2, 3.3, 3.3, 3.4, 3.4, 3.4,\] \[3.4, 3.5, 3.5, 3.5, 3.5, 3.6, 3.6, 3.7, 3.7, 3.8,\] \[3.8, 3.8, 3.8, 4.0, 4.0\]

The following frequency table gives the distribution of the variable high school GPA (with values rounded to nearest 0.5). Fill in the table and answer the following questions:

GPA Frequency Relative frequency Cumulative RF
2.0 2 0.06
2.5 1
3.0 0.43
3.5 14 0.4
4.0 6 0.17

\({\bf (11)}\) Which statistic is more resistant to outliers, the mean or median? Why?

\({\bf (12)}\) Describe the shape of the following distributions and for each distribution identify if the mean will be larger, smaller or the same as the median.

(a)

(b)

(c)

\({\bf (13)}\) Consider the following four sets of observations of a quantitative variable \(x\). For your convenience the observations have been sorted in increasing order. Match datasets \(1-4\) with the correct histogram (labeled \(A - D\))

\[\text{Dataset 1} = \{0.1, 1.1, 2.6, 2.7, 3.4, 3.4, 4.1, 4.4, 8.8, 9.6\}\] \[\text{Dataset 2}= \{0.1, 0.3, 1.2, 2.4, 4.4, 4.5, 8.0, 8.9, 9.3, 9.3\}\] \[\text{Dataset 3} = \{1.1, 3.8, 5.3, 6.0, 6.2, 6.9, 7.9, 7.9, 8.1, 8.7\}\] \[\text{Dataset 4} = \{3.4, 4.5, 5.4, 5.6, 7.0, 8.5, 8.9, 9.2, 9.7, 9.7\}\]

\({\bf (14)}\) Consider the following set of 10 observations of a variable \(X\) sorted from least to greatest: \[3.3, 3.8, 4.0, 4.8, 4.8, 5.1, 5.2, 5.6, 5.7, 6.9\] Use the data to answer parts a-b

\({\bf (15)}\) Consider the following \(n = 20\) observations of the sugar and sodium content of several popular cereal brands and answer questions a - g:

Brand Sodium (mg) Sugar (g) Type
Frosted Mini Wheats 0 11 A
Raisin Bran 340 18 A
All Bran 70 5 A
Apple Jacks 140 14 C
Cap’n Crunch 200 12 C
Cheerios 180 1 C
Cinnamon Toast Crunch 210 10 C
Crackling Oat Bran 150 16 A
Fiber One 100 0 A
Frosted Flakes 130 12 C
Froot Loops 140 14 C
Honey Bunches of Oats 180 7 A
Honey Nut Cheerios 190 9 C
Life 160 6 C
Rice Krispies 290 3 C
Honey Smacks 50 15 A
Special K 220 4 A
Wheaties 180 4 A
Corn Flakes 200 3 A
Honeycomb 210 11 C