Question 1

Which of the following best describes the primary purpose of using descriptive statistics in a research study?

Accepted Answer

To summarize and visualize data in order to identify patterns and trends

Question 2

A medical researcher collects data on the blood pressure of 200 patients. Which statistical method should she use first to understand the general distribution of blood pressure in her sample?

Accepted Answer

Construct a histogram and compute measures such as mean and standard deviation

Question 3

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

Accepted Answer

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

Question 4

A pharmaceutical company wants to test if a new drug lowers cholesterol more effectively than the current standard. Which statistical concept is most appropriate for making a decision based on sample data?

Accepted Answer

Inferential statistics

Question 5

Suppose the probability of a randomly selected student passing a statistics exam is 0.8. What is the probability that two randomly selected students both pass the exam, assuming independence?

Accepted Answer

$$0.8 	imes 0.8 = 0.64$$

Question 6

Which of the following statements about the normal distribution is TRUE?

Accepted Answer

The mean, median, and mode are all equal

Question 7

A researcher wants to estimate the average height of all students at a university. She randomly selects 100 students and calculates a 95% confidence interval for the mean height. What does this interval represent?

Accepted Answer

If the sampling process is repeated many times, about 95% of the calculated intervals will contain the true mean height

Question 8

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

Accepted Answer

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

Question 9

A hospital administrator wants to know if there is a relationship between hours of nurse staffing and patient recovery rates. Which statistical method should be used to analyze this relationship?

Accepted Answer

Linear regression

Question 10

Which of the following is an example of a null hypothesis ($$H_0) in a $$hypothesis test?

Accepted Answer

$$H_0$$: The average test score is equal to 75

Question 11

A city planner wants to compare the mean commute times of two different neighborhoods. Which statistical test is most appropriate?

Accepted Answer

Two-sample t-test

Question 12

If the correlation coefficient $$r$$ between two variables is $$-0.85$$, what does this indicate?

Accepted Answer

There is a strong negative linear relationship between the variables

Question 13

A researcher is testing whether a coin is fair. She flips the coin 100 times and gets 60 heads. Which statistical concept should she use to determine if the coin is biased?

Accepted Answer

Hypothesis testing

Question 14

Which of the following is NOT a requirement for using the Central Limit Theorem?

Accepted Answer

The population distribution must be normal

Question 15

A study finds that the mean weight of a sample of 50 apples is 150 grams with a standard deviation of 10 grams. What is the standard error of the mean?

Accepted Answer

$$\frac{10}{\sqrt{50}} = 1.41$$

Question 16

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

Accepted Answer

A parameter describes a population, while a statistic describes a sample

Question 17

A teacher wants to know if a new curriculum affects student performance. She randomly assigns students to two groups: one with the new curriculum and one with the old. Which type of study is this?

Accepted Answer

Experimental study

Question 18

Which of the following is the correct formula for the slope $$b_1 in $$simple linear regression, where $$x$$ and $$y$$ are variables and $$\bar{x}$$ and $$\bar{y}$$ are their means?

Accepted Answer

$$b_1$$ = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x}$$)^2$$}$$

Question 19

A researcher is interested in the relationship between hours studied and exam scores. She finds $$r = 0.6. $$What percentage of the variation in exam scores can be explained by hours studied?

Accepted Answer

36%

Question 20

Which of the following is an example of using probability concepts to make a reasonable conclusion in a real-world scenario?

Accepted Answer

Calculating the likelihood of rain tomorrow based on weather data

STA 2023 Statistical Methods: Course Overview and Key Concepts

Guida di studio - Domande di pratica

Study guide - Flashcard