Question 1

A pharmaceutical company wants to test the effectiveness of a new drug. They randomly assign 100 patients to receive the drug and another 100 to receive a placebo, then compare the outcomes. What type of study is this?

Accepted Answer

A designed experiment

Question 2

Which of the following best describes a simple random sample?

Accepted Answer

A sample in which every possible sample of the same size has an equal chance of being selected

Question 3

A researcher wants to study the average commute time of university students. She divides the students into groups based on their major and randomly selects students from each group. What sampling method is she using?

Accepted Answer

Stratified sampling

Question 4

Which of the following variables is discrete?

Accepted Answer

The number of cars in a parking lot

Question 5

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

Accepted Answer

$$ \frac{2+4+4+6+8}{5} = 4.8 $$

Question 6

A frequency distribution is constructed for the number of books read by students in a month. Which type of variable is being summarized?

Accepted Answer

Discrete quantitative

Question 7

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

Accepted Answer

It is always one of the data values

Question 8

A data set has a mean of 50 and a standard deviation of 5. What is the z-score for a value of 60?

Accepted Answer

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

Question 9

Which of the following best describes the difference between descriptive and inferential statistics?

Accepted Answer

Descriptive statistics summarize data; inferential statistics make predictions or inferences about a population based on a sample

Question 10

A researcher collects data on the favorite colors of 100 children. Which type of variable is 'favorite color'?

Accepted Answer

Qualitative (categorical)

Question 11

Which of the following is the formula for the sample variance $$ s^2$  of a $$data set with $$ n $$ values $$ x_1$, x_2$, ..., x_n $$ and sample mean $$ \overline{x} $$?

Accepted Answer

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

Question 12

A boxplot is most useful for identifying which of the following?

Accepted Answer

Outliers and the spread of the data

Question 13

A data set is right-skewed. Which of the following is most likely true?

Accepted Answer

The mean is greater than the median

Question 14

Which of the following is the correct formula for the least-squares regression line for predicting $$ y $$ from $$ x $$?

Accepted Answer

$$ \hat{y} = b_0$ + b_1$ x $$

Question 15

A study finds a correlation coefficient $$ r = -0.85 $$ between hours spent watching TV and exam scores. What does this indicate?

Accepted Answer

There is a strong negative linear relationship between hours spent watching TV and exam scores

Question 16

Which of the following best describes the coefficient of determination $$ R^2$ $$?

Accepted Answer

It represents the proportion of the variance in the dependent variable that is predictable from the independent variable

Question 17

A hospital administrator wants to estimate the average length of stay for patients. She randomly selects 5 departments and surveys all patients in those departments. What sampling method is this?

Accepted Answer

Cluster sampling

Question 18

Which of the following is a real-world example of using inferential statistics?

Accepted Answer

Estimating the average income of all households in a city based on a sample

Question 19

If a data set has the following five-number summary: minimum = 10, Q1 = 20, median = 30, Q3 = 40, maximum = 50, what is the interquartile range (IQR)?

Accepted Answer

$$ IQR = Q_3$ - Q_1$ = 40 - 20 = 20 $$

Question 20

A researcher wants to use systematic sampling to select a sample of 50 from a population of 500. What is the sampling interval $$ k $$?

Accepted Answer

$$ k = \frac{500}{50} = 10 $$

Statistics Study Guide: Key Concepts, Terms, and Skills

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