Q: A boxplot is constructed for a data set with $$Q1 = 20$$, $$Q3 = 40$$, and $$IQR = 20. $$What is the upper fence for outliers?

$$Q3 + 1.5 \times IQR = 40 + 1.5 \times 20 = 70$$

Question 1

A researcher wants to summarize the distribution of annual incomes for a group of people. The data is strongly right-skewed with several high-income outliers. Which measures of center and spread should the researcher use?

Accepted Answer

Median and interquartile range (IQR)

Question 2

A survey is conducted by posting a link online and allowing anyone to respond. Which sampling method is used, and what is the most likely source of bias?

Accepted Answer

Voluntary response sample; voluntary response bias

Question 3

Given the data set: 3, 7, 8, 12, 15, 18, 21, 24. What is the interquartile range (IQR)?

Accepted Answer

Question 4

A distribution is symmetric with no strong outliers. Which summary statistics are most appropriate?

Accepted Answer

Mean and standard deviation

Question 5

A researcher randomly selects 3 classrooms from a university and surveys every student in those rooms. Which sampling method is this?

Accepted Answer

Cluster sample

Question 6

If every value in a data set is increased by 7, what happens to the mean and standard deviation?

Accepted Answer

Mean increases by 7; standard deviation stays the same

Question 7

A Normal distribution has mean $$\mu = 60$$ and standard deviation $$\sigma = 10. $$What interval contains approximately 95% of the data?

Accepted Answer

$$60 \pm 2(10)$$, or 40 to 80

Question 8

A student scores 85 on a test where the mean is 70 and the standard deviation is 10. What is the student's z-score?

Accepted Answer

$$z = \frac{85 - 70}{10} = 1.5$$

Question 9

Which statement about correlation $$r is $$correct?

Accepted Answer

Correlation $$r$$ has no units and measures linear strength and direction

Question 10

A regression equation is $$\hat{y} = 5 + 2x. $$What does the slope mean in context?

Accepted Answer

For each 1-unit increase in $$x$$, predicted $$y$$ increases by 2 units on average

Question 11

A scatterplot shows a strong positive linear relationship between hours studied and exam score, but one student who studied a lot scored very low. What effect does this outlier have?

Accepted Answer

It decreases the correlation $$r$$

Question 12

A sample survey is conducted by randomly selecting students from each class year (freshman, sophomore, junior, senior). Which sampling method is this?

Accepted Answer

Stratified random sample

Question 13

In a randomized experiment testing a new drug, what is the main purpose of random assignment?

Accepted Answer

To balance lurking variables across treatment groups and support cause-and-effect conclusions

Question 14

A boxplot is constructed for a data set with $$Q1 = 20$$, $$Q3 = 40$$, and $$IQR = 20. $$What is the upper fence for outliers?

Accepted Answer

$$Q3 + 1.5 	imes IQR = 40 + 1.5 	imes 20 = 70$$

Question 15

A regression model predicts exam scores from hours studied. If a student actually scored 90 but the model predicted 85, what is the residual?

Accepted Answer

$$90 - 85 = +5$$

Question 16

Which of the following is NOT a source of bias in sample surveys?

Accepted Answer

Random assignment

Question 17

A distribution of test scores is left-skewed. Which statement is true?

Accepted Answer

Mean is less than median

Question 18

A timeplot is best used for which type of data?

Accepted Answer

Values measured over time to observe trends or cycles

Question 19

Which statement about $$R^2 in $$regression is correct?

Accepted Answer

$$R^2 is $$the percent of variation in $$y$$ explained by the linear model using $$x$$

Question 20

A researcher observes existing conditions without assigning treatments. What type of study is this, and what conclusion can be drawn?

Accepted Answer

Observational study; can show association but not causation

Introductory Statistics: Study Notes for Test 1 (Chapters 1–2, 4–5, 10–11)

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