Question 1

A pharmaceutical company finds a new drug reduces blood pressure by an average of 1 mmHg with a p-value of 0.0001. Which statement best describes this result?

Accepted Answer

The result is statistically significant but may not be practically significant.

Question 2

Which of the following is a statistic, not a parameter?

Accepted Answer

$$\bar{x}$$, the sample mean

Question 3

A researcher records the colors of cars in a parking lot. What type of data is this?

Accepted Answer

Categorical (qualitative)

Question 4

Which level of measurement is represented by temperature measured in degrees Celsius?

Accepted Answer

Interval

Question 5

A medical study randomly assigns patients to receive either a new drug or a placebo, then compares recovery rates. What type of study is this?

Accepted Answer

Experiment

Question 6

Given the following data: 2, 4, 4, 6, 8, what is the midrange?

Accepted Answer

$$\frac{2 + 8}{2} = 5$$

Question 7

Which measure of center is most resistant to outliers?

Accepted Answer

Median

Question 8

A dataset is highly skewed to the right. Which summary statistics should you report?

Accepted Answer

Median and interquartile range (IQR)

Question 9

If a value has a z-score of $$z = 2.5$$, what does this indicate?

Accepted Answer

The value is 2.5 standard deviations above the mean.

Question 10

Which formula correctly calculates the sample variance $$s^2$$ for a dataset of $$n$$ values $$x_1$$, $$x_2$$, ..., x_n$$ with sample mean $$\bar{x}$$?

Accepted Answer

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

Question 11

A boxplot shows a data set with a long whisker on the right. What does this suggest about the data?

Accepted Answer

The data is skewed to the right.

Question 12

Which of the following is the correct formula for the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$

Question 13

A student rolls a fair six-sided die. What is the classical probability of rolling a 4?

Accepted Answer

$$\frac{1}{6}$$

Question 14

If $$P(A) = 0.3$$, $$P(B) = 0.5$$, and $$A$$ and $$B$$ are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$0.15$$

Question 15

A bag contains 5 red and 7 blue marbles. If you draw one marble at random, what is the probability it is red?

Accepted Answer

$$\frac{5}{12}$$

Question 16

Which of the following best describes the difference between relative frequency and classical probability?

Accepted Answer

Relative frequency is based on data; classical assumes all outcomes are equally likely.

Question 17

If $$P(A) = 0.4$$ and $$P(B) = 0.5$$, and $$A$$ and $$B$$ are mutually exclusive, what is $$P(A \cup B)$$?

Accepted Answer

$$0.9$$

Question 18

A hospital tests for a rare disease. The probability a randomly selected patient has the disease is 0.01. What is the probability a patient does NOT have the disease?

Accepted Answer

$$0.99$$

Question 19

Which formula gives the conditional probability of $$A$$ given $$B$$?

Accepted Answer

$$P(A \mid B) = \frac{P(A \cap B)}{P(B)}$$

Question 20

A class of 30 students has test scores with a mean of 75 and a standard deviation of 5. According to the Empirical Rule, about 95% of scores should fall between:

Accepted Answer

$$65$$ and $$85$$

Statistics Fundamentals: Concepts, Data, and Probability

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