Q: A store has 9 shirt options, 6 pants options, and 5 sock options. You will select 2 shirts, 3 pants, and 1 pair of socks. How many combinations are possible?

$$\binom{9}{2} \times \binom{6}{3} \times \binom{5}{1} = 36 \times 20 \times 5 = 3600$$

Q: Given the following contingency table for a medical test: Covid+ and +test: 30 Covid+ and -test: 6 Covid- and +test: 3 Covid- and -test: 92 What is the probability that a randomly selected individual tests positive given that they have Covid?

$$P(+\text{ test} | \text{Covid} +) = \frac{30}{36}$$

Q: If the geometric mean return over 3 years is 9.943%, and the returns for year 1 and 2 are 15% and 8%, what is the return for year 3 (Y)?

$$Y = \$$left(1.09943^3$$ \div (1.15 \times 1.08)\right) - 1 \approx 6.8\%$$

Question 1

Which of the following is an example of a parameter rather than a statistic?

Accepted Answer

The average height of all students in a university

Question 2

A researcher wants to study the average commute time of employees in a large company. She randomly selects 5 departments, then surveys every employee in those departments. Which sampling method is she using?

Accepted Answer

Cluster sampling

Question 3

Which of the following best describes a nonresponse error?

Accepted Answer

When selected individuals do not participate in the survey

Question 4

Given the following data set: 80, 32, 90, 95, 67, 67, 68, 72, 31, 35, 39, 60. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 72 - 35 = 37$$

Question 5

A histogram is most appropriate for displaying which type of data?

Accepted Answer

Continuous quantitative data

Question 6

If the mean of a data set is 50, the standard deviation is 5, and a value is 65, what is the z-score of this value?

Accepted Answer

$$z = \frac{65 - 50}{5} = 3$$

Question 7

According to Chebyshev's theorem, at least what percentage of data values must fall within 2 standard deviations of the mean for any data set?

Accepted Answer

$$1 - \frac{1}{2^2$} = 0.75 or 75$$%

Question 8

A fair die is rolled twice. Let $$A be $$the event that a 3 is rolled exactly once, and $$B be $$the event that the sum of the two rolls is less than 7. What is $$P(A \cup B)$$?

Accepted Answer

$$P(A \cup B) = \frac{23}{36}$$

Question 9

Suppose a classroom has 10 students and a teacher will randomly select 3. How many combinations are possible?

Accepted Answer

$$\binom{10}{3} = 120$$

Question 10

A store has 9 shirt options, 6 pants options, and 5 sock options. You will select 2 shirts, 3 pants, and 1 pair of socks. How many combinations are possible?

Accepted Answer

$$\binom{9}{2} 	imes \binom{6}{3} 	imes \binom{5}{1} = 36 	imes 20 	imes 5 = 3600$$

Question 11

Given the following contingency table for a medical test:

Covid+ and +test: 30
Covid+ and -test: 6
Covid- and +test: 3
Covid- and -test: 92

What is the probability that a randomly selected individual tests positive given that they have Covid?

Accepted Answer

$$P(+	ext{ test} | 	ext{Covid} +) = \frac{30}{36}$$

Question 12

A data set has a mean of 100 and a standard deviation of 10. According to the empirical rule, approximately what percentage of data falls between 80 and 120?

Accepted Answer

About 95%

Question 13

If the geometric mean return over 3 years is 9.943%, and the returns for year 1 and 2 are 15% and 8%, what is the return for year 3 (Y)?

Accepted Answer

$$Y = \$$left(1.09943^3$$ \div (1.15 	imes 1.08)ight) - 1 \approx 6.8\%$$

Question 14

Which of the following statements about the correlation coefficient $$r is $$TRUE?

Accepted Answer

$$r$$ measures the strength and direction of a linear relationship between two variables.

Question 15

A Venn diagram is most useful for which of the following tasks?

Accepted Answer

Visualizing the relationships and intersections between events

Question 16

Suppose you have two jars: Jar I has 20 green marbles and 5 blue marbles, Jar II has 25 green marbles and 5 blue marbles. The probability of selecting Jar II is 0.40. What is the probability that a blue marble is chosen?

Accepted Answer

$$P(	ext{blue}) = 0.60 	imes \frac{5}{25} + 0.40 	imes \frac{5}{30} = 0.12 + 0.0667 = 0.1867$$

Question 17

Which of the following is NOT a property of the mean?

Accepted Answer

It is always resistant to outliers.

Question 18

If two events are disjoint, which of the following is true?

Accepted Answer

$$P(A \cap B) = 0$$

Question 19

A theme park has 8 roller coasters and you can only ride 4 of them in one day, riding each only once. How many ways are there to order the roller coaster rides?

Accepted Answer

$$P(8,4) = \frac{8!}{(8-4)!} = 1680$$

Statistics Study Guide: Key Concepts, Methods, and Practice Problems

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