Question 1

Which of the following best describes the Central Limit Theorem?

Accepted Answer

It states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the population's distribution.

Question 2

A pharmaceutical company wants to test a new drug. Which of the following best illustrates a designed experiment?

Accepted Answer

The company randomly assigns patients to receive either the new drug or a placebo and compares the outcomes.

Question 3

Which formula is used to calculate the sample mean $$\bar{x}$$ for a set of $$n$$ data values $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

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

Question 4

A hospital records the number of patients admitted each day for a month. Which type of data is this?

Accepted Answer

Discrete

Question 5

Which of the following is NOT a requirement for a binomial distribution?

Accepted Answer

The number of successes must be greater than the number of failures.

Question 6

A researcher wants to estimate the average height of adult males in a city. Which sampling method would best reduce bias?

Accepted Answer

Random sampling

Question 7

If the probability of an event $$A is$$ $$P(A) = 0.3$$, what is the probability that $$A$$ does NOT occur?

Accepted Answer

$$0.7$$

Question 8

Which formula is used to calculate the standard deviation $$s of a $$sample?

Accepted Answer

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

Question 9

A boxplot is most useful for:

Accepted Answer

Visualizing the spread, median, and potential outliers in a dataset

Question 10

Which formula represents the least squares regression line for predicting $$y$$ from $$x$$?

Accepted Answer

$$y = a + bx$$

Question 11

A student rolls a fair six-sided die 60 times and records the number of times a 4 appears. Which statistical concept is illustrated by the result approaching the theoretical probability as the number of rolls increases?

Accepted Answer

Law of Large Numbers

Question 12

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

Accepted Answer

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

Question 13

Which of the following best describes an observational study?

Accepted Answer

Researchers observe subjects without influencing them and record data.

Question 14

A medical researcher tests whether a new vaccine is effective. Which hypothesis test should be used to compare the proportion of patients who develop immunity in the vaccine group versus the control group?

Accepted Answer

Two-sample proportion test

Question 15

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

Accepted Answer

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

Question 16

Which of the following is a real-world example of a continuous random variable?

Accepted Answer

The height of students in a classroom

Question 17

A correlation coefficient $$r of$$ $$-0.85$$ between hours studied and exam score indicates:

Accepted Answer

A strong negative linear relationship

Question 18

Which formula is used to calculate the z-score for a value $$x in a $$dataset with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

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

Question 19

A university wants to compare the average GPA of students in two different majors. Which statistical test is most appropriate?

Accepted Answer

Two-sample t-test for means

Statistics I (MTH 245) Syllabus and Course Overview Study Guide

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