Question 1

Which of the following best describes the purpose of using graphical presentations in statistics?

Accepted Answer

To visually summarize and reveal patterns, trends, and outliers in data.

Question 2

A researcher wants to compare the average test scores between two different teaching methods. Which statistical test is most appropriate?

Accepted Answer

Two-sample t-test

Question 3

Which of the following is NOT a measure of central tendency?

Accepted Answer

Standard deviation

Question 4

Suppose a dataset is highly skewed to the right. Which measure of central tendency is most likely to be affected?

Accepted Answer

Mean

Question 5

A pharmaceutical company tests a new drug and finds a p-value of 0.03 when comparing it to a placebo. At a significance level of $$\alpha = 0.05$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is evidence the drug is effective.

Question 6

Which formula correctly represents the standard deviation of a sample?

Accepted Answer

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

Question 7

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

Accepted Answer

It is defined by its mean and standard deviation.

Question 8

A student calculates a 95% confidence interval for the mean height of sunflowers in a field as (150 cm, 170 cm). What does this interval mean?

Accepted Answer

We are 95% confident that the population mean height is between 150 cm and 170 cm.

Question 9

Which of the following is a key assumption for performing a linear regression analysis?

Accepted Answer

The relationship between variables is linear.

Question 10

A fair coin is flipped 5 times. What is the probability of getting exactly 3 heads? Use the binomial formula.

Accepted Answer

$$P = \binom{5}{3} (0.5)^3$ (0.5)^2$ = 0.3125$$

Question 11

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting a true null hypothesis.

Question 12

A researcher wants to test if a new fertilizer increases crop yield. Which is the most appropriate null hypothesis?

Accepted Answer

$$H_0$$: \mu_{fertilizer} = \mu_{no\ fertilizer}$$

Question 13

Which of the following is an example of a nonparametric statistical test?

Accepted Answer

Chi-square test

Question 14

A sample of 100 students has a mean test score of 80 with a standard deviation of 10. What is the standard error of the mean?

Accepted Answer

$$SE = \frac{10}{\sqrt{100}} = 1$$

Question 15

Which of the following best describes the purpose of analysis of variance (ANOVA)?

Accepted Answer

To compare the means of three or more groups.

Question 16

Which formula represents the correlation coefficient between two variables X and Y?

Accepted Answer

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

Question 17

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

Accepted Answer

Chi-square test for independence

Question 18

Which of the following is a key difference between a population and a sample?

Accepted Answer

A sample is a subset of a population.

Question 19

If the probability of rain on any given day is 0.2, what is the probability that it will rain on exactly 2 out of 5 consecutive days?

Accepted Answer

$$P = \binom{5}{2} (0.2)^2$ (0.8)^3$ = 0.2048$$

Question 20

Which of the following best describes the meaning of a p-value in hypothesis testing?

Accepted Answer

The probability of observing data as extreme as, or more extreme than, the observed data, assuming the null hypothesis is true.

Introductory Statistics Course Syllabus and Study Guide

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드