Question 1

Which of the following best describes the difference between a population and a sample in statistics?

Accepted Answer

A population includes all members of a defined group, while a sample is a subset of the population selected for analysis.

Question 2

Suppose a researcher wants to estimate the average height of all university students. She randomly selects 100 students and calculates their mean height. Which statistical concept is illustrated by her calculation?

Accepted Answer

Statistic

Question 3

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

Accepted Answer

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

Question 4

A pharmaceutical company tests a new drug on a group of patients and records whether each patient recovers (yes/no). What type of variable is 'recovery status'?

Accepted Answer

Qualitative, nominal

Question 5

Which of the following is the correct formula for the probability of the union of two events $$A$$ and $$B$$?

Accepted Answer

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

Question 6

A fair six-sided die is rolled twice. What is the probability that both rolls result in an even number?

Accepted Answer

$$\frac{1}{4}$$

Question 7

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

Accepted Answer

It is skewed to the right.

Question 8

A researcher wants to test whether a new teaching method improves exam scores. Which statistical test is most appropriate if the exam scores are normally distributed and the researcher compares the means of two independent groups?

Accepted Answer

Independent samples t-test

Question 9

Given a regression equation $$y = 2 + 3x$$, what is the predicted value of $$y$$ when $$x = 4$$?

Accepted Answer

$$y = 14$$

Question 10

Which of the following is the correct formula for a 95% confidence interval for the population mean $$\mu$$ when the population standard deviation $$\sigma is $$known?

Accepted Answer

$$\overline{x} \pm z_{0.025} \frac{\sigma}{\sqrt{n}}$$

Question 11

A hospital administrator wants to know if there is an association between gender (male/female) and recovery from surgery (yes/no). Which statistical test should be used?

Accepted Answer

Chi-square test of independence

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.

Question 13

Which of the following is NOT an assumption of the simple linear regression model?

Accepted Answer

The variance of the residuals increases with the independent variable.

Question 14

A researcher collects data on the number of hours studied and exam scores for 50 students. Which graphical method is most appropriate to display the relationship between these two variables?

Accepted Answer

Scatterplot

Question 15

Which of the following best describes the Central Limit Theorem?

Accepted Answer

The distribution of sample means approaches a normal distribution as the sample size increases, regardless of the population's distribution.

Question 16

A company claims that their batteries last an average of 100 hours. A consumer group tests 36 batteries and finds a sample mean of 98 hours with a standard deviation of 6 hours. What is the value of the test statistic for testing the company's claim?

Accepted Answer

$$z = \frac{98 - 100}{6/\sqrt{36}} = -2$$

Question 17

Which of the following is the correct formula for the expected value $$E(X) of a $$discrete random variable $$X$$ with possible values $$x_1$$, $$x_2$$, ..., x_n$$ and probabilities p_1$, p_2$, ..., p_n$$?

Accepted Answer

$$E(X) = \sum_{i=1}^{n} x_i p_i$$

Question 18

A medical test for a disease has a sensitivity of 90% and a specificity of 95%. If a patient tests positive, which statistical concept helps determine the probability that the patient actually has the disease?

Accepted Answer

Positive predictive value (using Bayes' theorem)

Question 19

Which of the following is the correct formula for the standard error of the mean (SEM) for a sample of size $$n$$ with standard deviation $$s$$?

Accepted Answer

$$SEM = \frac{s}{\sqrt{n}}$$

Statistics Course Sequence and Topics Overview

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드