Question 1

Which of the following best describes the difference between descriptive and inferential statistics?

Accepted Answer

Descriptive statistics summarize and organize data, while inferential statistics use data from a sample to make generalizations about a population.

Question 2

A researcher collects the heights (in cm) of 100 university students. Which graphical display would be most appropriate to visualize the distribution of this quantitative variable?

Accepted Answer

Histogram

Question 3

Suppose the mean score on a statistics exam is 75 with a standard deviation of 8. If a student scored 91, what is their z-score?

Accepted Answer

$$z = \frac{91 - 75}{8} = 2$$

Question 4

Which of the following is NOT a property of the normal distribution?

Accepted Answer

It is skewed to the right.

Question 5

A fair coin is flipped 10 times. What is the probability of getting exactly 6 heads? (Use the binomial formula.)

Accepted Answer

$$P(X=6) = \binom{10}{6} (0.5)^6$ (0.5)^4$

Question 6

Which of the following statements about the sampling distribution of the sample mean is TRUE?

Accepted Answer

Its mean is equal to the population mean.

Question 7

A researcher wants to test if a new medication lowers blood pressure. Which is the appropriate null hypothesis ($$H_0) $$for a one-sample mean test?

Accepted Answer

$$H_0$$: \mu = \$$mu_0$$

Question 8

Which formula is used to calculate the standard error of the mean for a sample of size $$n$$ from a population with standard deviation $$\sigma$$?

Accepted Answer

$$SE = \frac{\sigma}{\sqrt{n}}$$

Question 9

A 95% confidence interval for a population mean is calculated as (12.5, 17.5). Which of the following is a correct interpretation?

Accepted Answer

We are 95% confident that the population mean is between 12.5 and 17.5.

Question 10

Which of the following scenarios best illustrates the use of a paired t-test?

Accepted Answer

Comparing the mean blood pressure of patients before and after taking a medication.

Question 11

If the $$p-$$value for a hypothesis test is 0.03 and the significance level $$\alpha is 0.05$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 12

Which equation represents the simple linear regression model?

Accepted Answer

$$y = \$$beta_0$$ + \$$beta_1$$ x + \epsilon$$

Question 13

A study finds a correlation coefficient $$r = 0.85$$ between hours studied and exam scores. What does this indicate?

Accepted Answer

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

Question 14

Which of the following is an example of a random variable?

Accepted Answer

The outcome of rolling a fair six-sided die.

Question 15

Which formula is used to calculate the probability of $$k$$ successes in $$n$$ independent Bernoulli trials with probability $$p of $$success?

Accepted Answer

$$P(X = k) = \binom{n}{k} p^k (1-p$$)^{n-k}$$

Question 16

A sample of 50 students has a mean height of 170 cm and a standard deviation of 10 cm. What is the 95% confidence interval for the mean height? (Use $$z^* = 1.96)$$

Accepted Answer

$$170 \pm 1.96 	imes \frac{10}{\sqrt{50}}$$

Question 17

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 18

A researcher wants to compare the average test scores of two independent groups. Which statistical test should be used?

Accepted Answer

Two-sample t-test

Question 19

Which of the following is a correct interpretation of a $$p-$$value?

Accepted Answer

The probability of observing data as extreme as the sample, assuming the null hypothesis is true.

Question 20

Which of the following is an example of using statistics in a real-world context?

Accepted Answer

A hospital uses patient data to determine if a new treatment is effective.

STAT 101 24 – Winter 2026: Course Syllabus and Overview

스터디 가이드 - 연습 문제

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