Question 1

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

Accepted Answer

Designed experiment

Question 2

Which of the following best describes a simple random sample?

Accepted Answer

A sample where every individual in the population has an equal chance of being selected

Question 3

A researcher wants to study the average commute time of university students. She divides students by major and randomly selects 10 students from each major. What sampling method is she using?

Accepted Answer

Stratified sampling

Question 4

Which formula correctly calculates the sample mean $$\bar{x}$$ for a data set with $$n$$ values $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

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

Question 5

A hospital wants to estimate the average length of stay for patients. They select every 5th patient admitted during a month. What type of sampling is this?

Accepted Answer

Systematic sampling

Question 6

Which of the following is a quantitative variable?

Accepted Answer

Number of siblings

Question 7

Given the data set: 2, 4, 4, 5, 7, what is the median?

Accepted Answer

4

Question 8

A frequency distribution for exam scores is shown below: 50-59: 2 students, 60-69: 5 students, 70-79: 8 students, 80-89: 3 students. What is the relative frequency of the 70-79 interval?

Accepted Answer

$$\frac{8}{18}$$

Question 9

Which formula is used to calculate the sample variance $$s^2$$ for a data set with $$n$$ values and sample mean $$\bar{x}$$?

Accepted Answer

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

Question 10

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 11

Which of the following best describes a population in statistics?

Accepted Answer

All individuals or items that are the subject of a statistical study

Question 12

A biologist records the heights of 100 plants. Which measure of center is least affected by an extremely tall outlier?

Accepted Answer

Median

Question 13

Which formula represents the least-squares regression line for predicting $$y$$ from $$x$$?

Accepted Answer

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

Question 14

A scatterplot of two variables shows a strong positive linear relationship. Which value is most likely for the Pearson correlation coefficient $$r$$?

Accepted Answer

$$r = 0.90$$

Question 15

A teacher wants to compare test scores between two classes. Which graphical display is most appropriate for comparing the distributions?

Accepted Answer

Box-and-whisker plot

Question 16

Which of the following is a discrete variable?

Accepted Answer

Number of cars in a parking lot

Question 17

A sample of 20 patients has a mean cholesterol level of 200 mg/dL and a sample standard deviation of 20 mg/dL. What is the sample variance?

Accepted Answer

$$s^2 = 400$

Question 18

Which of the following statements about the coefficient of determination $$R^2 is $$correct?

Accepted Answer

$$R^2$$ measures the proportion of variation in $$y$$ explained by $$x$$

Question 19

A researcher collects data on the number of hours students study and their exam scores. She finds $$r = 0.75. $$What does this indicate?

Accepted Answer

There is a strong positive linear relationship between hours studied and exam scores

Foundations of Statistics: Study Guide and Key Terms

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