Question 1

A study investigates whether a new medication reduces the frequency of migraines. 400 patients are randomly assigned to receive either the medication or a placebo. 205 out of 270 patients in the medication group report improvement, while 140 out of 230 in the placebo group report improvement. What is the correct interpretation of these results?

Accepted Answer

The medication is effective because a higher percentage of patients improved in the medication group compared to the placebo group.

Question 2

In a controlled experiment studying the effects of diet restriction on dogs, which of the following best describes the 'treatment variable'?

Accepted Answer

The amount of food intake

Question 3

A histogram of SAT Math scores for a sample of students is unimodal and skewed left. Which of the following is most likely true about the distribution?

Accepted Answer

Most students scored very high, with a few low outliers.

Question 4

Which of the following best describes an observational study?

Accepted Answer

Researchers observe subjects without assigning treatments and record outcomes.

Question 5

Given the following data for heights (in inches) of 4 students: 68, 67, 62, 74. Calculate the mean height $\bar{x}$.

Accepted Answer

$\bar{x} = \frac{68 + 67 + 62 + 74}{4} = 67.75$

Question 6

Which of the following variables is categorical?

Accepted Answer

Sandwich choice (Hamburger, Cheeseburger, Double Double)

Question 7

A histogram of ages at US presidential inauguration is described as 'unimodal, roughly symmetric.' What does this imply about the distribution?

Accepted Answer

There is one peak and the data is evenly distributed around the center.

Question 8

Which of the following is the correct formula for the sample standard deviation $s$ of $n$ data points $x_1, x_2, ..., x_n$ with mean $\bar{x}$?

Accepted Answer

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

Question 9

In a study, the variable 'Political Party' is recorded for each US President. What is the most appropriate type of graph to display the distribution of this variable?

Accepted Answer

Bar chart

Question 10

A researcher wants to determine if a new teaching method improves test scores. She randomly assigns students to either the new method or the traditional method and compares their final exam scores. What type of study is this?

Accepted Answer

Controlled experiment

Question 11

A sample of 50 students has Verbal SAT scores with a histogram that is more spread out than the Math SAT scores. What does this indicate?

Accepted Answer

Verbal SAT scores are more variable than Math SAT scores.

Question 12

Which of the following best describes the median?

Accepted Answer

The middle value when the data is ordered from least to greatest.

Question 13

In a study of diet restriction in dogs, which of the following is a response variable?

Accepted Answer

Body fat

Question 14

A bar chart is most appropriate for which type of variable?

Accepted Answer

Categorical

Question 15

If a data set has a mean of 55, a median of 55, a standard deviation of 6.6, and an interquartile range of 7, what can you infer about the shape of the distribution?

Accepted Answer

The distribution is likely symmetric.

Question 16

Which of the following is NOT a characteristic of a controlled experiment?

Accepted Answer

Observation without intervention

Question 17

A researcher records the eye color (Brown, Blue, Hazel) of students in a class. What type of variable is eye color?

Accepted Answer

Categorical

Question 18

Which of the following best describes the interquartile range (IQR)?

Accepted Answer

The difference between the third quartile ($Q_3$) and the first quartile ($Q_1$): $IQR = Q_3 - Q_1$

Question 19

A study finds that the mean height of male students is 69 inches and the mean height of female students is 64 inches. What is the best way to describe the difference in means?

Accepted Answer

There is a 5 inch difference in mean height between male and female students.

Question 20

Which of the following is a common misconception when interpreting the results of an observational study?

Accepted Answer

Assuming that correlation implies causation.

Fundamental Concepts and Applications in Introductory Statistics

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