Question 1

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is a numerical characteristic of a population, while a statistic is a numerical characteristic of a sample.

Question 2

A researcher wants to estimate the average height of all students at a university. She randomly selects 100 students and calculates their average height. In this scenario, what is the sample and what is the population?

Accepted Answer

Sample: The 100 selected students; Population: All students at the university.

Question 3

Which sampling method is most likely to produce a biased sample?

Accepted Answer

Voluntary response sampling

Question 4

Suppose a population is divided into subgroups based on age, and a simple random sample is taken from each subgroup. What type of sampling is this?

Accepted Answer

Stratified random sampling

Question 5

A hospital administrator wants to estimate the average length of stay for patients. She records the length of stay for every 10th patient admitted. What type of sampling is this?

Accepted Answer

Systematic sampling

Question 6

Which of the following is a categorical (qualitative) variable?

Accepted Answer

Province in which a person resides

Question 7

Given the data set: 2, 4, 6, 8, 10, what is the mean?

Accepted Answer

$$ \frac{2+4+6+8+10}{5} = 6 $$

Question 8

Which formula correctly calculates the sample variance $$ s^2$ $$ for a sample of $$ n $$ observations $$ x_1$, x_2$, ..., x_n $$ with sample mean $$ \bar{x} $$?

Accepted Answer

$$ s^2$ = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2$}{n-1} $$

Question 9

A boxplot is useful for:

Accepted Answer

Displaying the five-number summary and identifying outliers

Question 10

If the sample mean is multiplied by a constant $$ b $$, what happens to the sample variance?

Accepted Answer

It is multiplied by $$ b^2$ $$

Question 11

Which of the following is NOT a measure of central tendency?

Accepted Answer

Range

Question 12

In a normal distribution, approximately what percentage of observations fall within two standard deviations of the mean?

Accepted Answer

About 95%

Question 13

Which formula gives the percent relative frequency for a category with frequency $$ f  in a $$sample of size $$ n $$?

Accepted Answer

$$ \frac{f}{n} 	imes 100\% $$

Question 14

Which of the following best describes confounding in an observational study?

Accepted Answer

Two variables are confounded if their effects on the response variable cannot be separated.

Question 15

A pharmaceutical company wants to test a new drug. They randomly assign patients to receive either the drug or a placebo and measure their blood pressure after treatment. What type of study is this?

Accepted Answer

Experiment

Question 16

Which of the following is the correct formula for the sample mean $$ \bar{x}  of$$ $$ n $$ observations $$ x_1$, x_2$, ..., x_n $$?

Accepted Answer

$$ \bar{x} = \frac{\sum_{i=1}^{n} x_i}{n} $$

Question 17

Which of the following statements about sampling is TRUE?

Accepted Answer

A biased sampling design can lead to misleading results even with a large sample size.

Question 18

If a data set has a mean of 50 and a standard deviation of 5, what is the z-score of an observation with value 60?

Accepted Answer

$$ z = \frac{60 - 50}{5} = 2 $$

Question 19

Which of the following is the best definition of the interquartile range (IQR)?

Accepted Answer

The difference between the third quartile and the first quartile: $$ IQR = Q_3$ - Q_1$ $$

STAT 2040 Study Notes: Chapters 1-4 (Sampling, Descriptive Statistics, Probability, Discrete Random Variables)

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