Question 1

Which of the following best describes the primary purpose of statistical methods in scientific research?

Accepted Answer

To analyze data and draw conclusions about populations based on samples.

Question 2

A researcher wants to estimate the average blood pressure of adults in a city. She randomly selects 100 adults and calculates the mean. Which statistical concept is she applying?

Accepted Answer

Inferential statistics

Question 3

Which formula correctly calculates the sample mean $$\bar{x}$$ for 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 tests a new drug on 200 patients and finds a statistically significant reduction in symptoms. What does 'statistically significant' mean in this context?

Accepted Answer

The observed reduction is unlikely to have occurred by random chance alone.

Question 5

Which of the following is the correct formula for the sample standard deviation $$s$$?

Accepted Answer

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

Question 6

A hospital administrator wants to compare the average length of stay for patients before and after a new policy. Which statistical test is most appropriate?

Accepted Answer

Paired t-test

Question 7

If the probability of a patient recovering from a surgery is 0.8, what is the probability that two randomly selected patients both recover?

Accepted Answer

$$0.8 	imes 0.8 = 0.64$$

Question 8

Which of the following statements about the null hypothesis $$H_0 is $$correct?

Accepted Answer

It represents the default assumption that no effect or difference exists.

Question 9

A student calculates a correlation coefficient $$r = 0.95$$ between hours studied and exam scores. What does this value indicate?

Accepted Answer

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

Question 10

Which formula represents the calculation of a z-score for a value $$x in a $$population with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 11

A medical researcher wants to know if a new treatment is more effective than the standard. She randomly assigns patients to two groups and compares outcomes. What type of study is this?

Accepted Answer

Experimental study

Question 12

Which of the following is NOT a requirement for a valid random sample?

Accepted Answer

Sample size must be larger than the population.

Question 13

A teacher wants to know if students who attend review sessions score higher on exams. She collects exam scores from students who did and did not attend. Which statistical method should she use?

Accepted Answer

Two-sample t-test

Question 14

Which formula is used to calculate the probability of either event A or event B occurring, if A and B are mutually exclusive?

Accepted Answer

$$P(A \cup B) = P(A) + P(B)$$

Question 15

A researcher finds a p-value of 0.03 when testing a hypothesis at the 0.05 significance level. What should she conclude?

Accepted Answer

Reject the null hypothesis.

Question 16

Which of the following best describes the central limit theorem?

Accepted Answer

The distribution of sample means approaches a normal distribution as sample size increases.

Question 17

A scientist collects data on plant growth under different light conditions. She wants to test if the mean growth differs among three groups. Which statistical test should she use?

Accepted Answer

ANOVA

Question 18

Which formula is used to calculate the confidence interval for a population mean when the population standard deviation is unknown?

Accepted Answer

$$\bar{x} \pm t^* \frac{s}{\sqrt{n}}$$

Question 19

A company wants to predict future sales based on advertising spending. Which statistical method is most appropriate?

Accepted Answer

Linear regression

Question 20

A student is asked to solve a multi-step problem: First, calculate the mean of the following data set: 2, 4, 6, 8, 10. Then, use the mean to calculate the z-score for the value 10, assuming the sample standard deviation is 3. What is the z-score?

Accepted Answer

$$z = \frac{10 - 6}{3} = 1.33$$

Statistics Course Syllabus and Success Guide

Guida di studio - Domande di pratica

Study guide - Flashcard