In Chapter 3 the data frame "ex.2", which contained information associated to the blood pressure of a sample of 150 men and women, was introduced. Let us assume that this sample was taken from an imaginary population of size 100,000 and let the information for all the members of this population be stored in a CSV file by the name "pop2.csv".

Read the content of the population file into an data frame under the name "pop.2". Applying the function "summary" to this data frame produces:

 > summary(pop.2) 

id

sex

age

Min. : 1000050

FEMALE:50032

Min. :20.00

1st Qu.: 3227517

MALE :49968

1st Qu.:32.00

Median : 5479268

Median :35.00

Mean : 5482739

Mean :34.98

3rd Qu.: 7721879

3rd Qu.:38.00

Max. : 9999889

Max. :54.00

bmi

systolic

diastolic

Min. : 9.986

Min. : 73.37

Min. : 24.77

1st Qu.:22.081

1st Qu.:116.33

1st Qu.: 72.62

Median :24.819

Median :124.64

Median : 81.27

Mean :24.984

Mean :125.02

Mean : 81.67

3rd Qu.:27.704

3rd Qu.:133.22

3rd Qu.: 90.30

Max. :46.232

Max. :191.65

Max. :152.34

group

HIGH :28126

LOW : 4215

NORMAL:67659

The variables in this data frame are the same variables that were included in the data frame "ex.2" of Chapter 3. The variables that are included in this data frame are:

id:

A numerical variable. A 7 digits number that serves as a unique identifier of the subject.

sex:

A factor variable. The sex of each subject. The values are either "MALE" or "FEMALE".

age:

A numerical variable. The age of each subject.

bmi:

A numerical variable. The body mass index of each subject.

systolic:

A numerical variable. The systolic blood pressure of each subject.

diastolic:

A numerical variable. The diastolic blood pressure of each subject.

group:

A factor variable. The blood pressure category of each subject. The values are "NORMAL" both the systolic blood pressure is within its normal range (between 90 and 139) and the diastolic blood pressure is within its normal range (between 60 and 89). The value is "HIGH" if either measurements of blood pressure are above their normal upper limits and it is "LOW" if either measurements are below their normal lower limits.

The next 6 questions correspond to a person that is sampled at random from this population. The answers below may be rounded up to two decimal places.

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The median age in this sample was:

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The variance of the diastolic blood pressure in this sample was:

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The standard deviation of the difference between the systolic and diastolic blood pressures was:Answer (Hint: Observe that the difference "pop.2$systolic - pop.2$diastolic" produces the difference between the two types of blood pressure for all the members in the population.)

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The largest BMI value in this sample was:

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The probability that someone sampled from this data will have normal blood pressure is:

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Mark the following statement as either TRUE or FALSE: The standard deviation of the difference between the systolic and diastolic blood pressures is equal to the difference between the standard deviation of systolic blood pressure and the standard deviation of diastolic blood pressure Answer.

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The Distribution of Y Value Probability 1.5 0.15 4 5.5 0.10 6 0.23 7.5 0.11 10 0.05 Complete the probabilities of the random variable Y in above table and compute

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P(Y < 5) equals

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P(Y not an integer) equals

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E(Y) equals

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The standard deviation of Y is equal to

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One selects an integer between 1 and 9 (including 1 and 9) at random. Let X be a random variable that obtains as a value the integer that was selected. The following questions correspond to this random variable. The Distribution of X Value Probability Complete table of distribution of X and compute:

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E(X) is equal to

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The variance of X is equal to

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The standard deviation of X is equal to

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Suppose that you are offered the following "deal." An impartial person selects an integer between 1 and 9 at random and you try to guess beforehand which number will be selected. If you guess wrong then you pay $1 and if you guess right then you win $10. Call the outcome of the game your "gain." (Note that if you pay money then your gain is negative.)

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In this game your probability of winning is

Select one:

a. Larger than your probability of losing.

b. Smaller than your probability of losing.

c. Equal to your probability of losing.

d. Unknown.

Clear my choice

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The expected gain in this game is

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