Q: A least-squares regression line is given by $$y = 2x + 5. $$What is the predicted value $$\hat{y}$$ when $$x = 4$$?

$$\hat{y} = 2 \times 4 + 5 = 13$$

Q: A sample of 10 values has $$Q_1 = 15$, Q_3$ = 25$$, and the maximum value is 40. What is the upper fence for outliers?

$$\text{Upper fence} = Q_3$ + 1.5 \times IQR = 25 + 1.5 \times (25 - 15) = 40$$

Question 1

A researcher wants to study the effect of a new drug on blood pressure. She randomly assigns 100 patients to receive either the drug or a placebo and measures their blood pressure after 4 weeks. Which of the following best describes this study?

Accepted Answer

It is a designed experiment because the researcher manipulates the explanatory variable (drug vs placebo).

Question 2

Which of the following variables is continuous?

Accepted Answer

The temperature measured in degrees Celsius.

Question 3

A survey asks students to rate their satisfaction with campus facilities as 'Poor', 'Fair', 'Good', or 'Excellent'. What is the level of measurement for this variable?

Accepted Answer

Ordinal

Question 4

A sample of 5 exam scores is: 70, 75, 80, 85, 90. What is the sample mean $$\bar{x}$$?

Accepted Answer

$$\bar{x} = \frac{70 + 75 + 80 + 85 + 90}{5} = 80$$

Question 5

Which sampling method is most likely to introduce sampling bias?

Accepted Answer

Convenience sampling

Question 6

A histogram is constructed for a set of exam scores. The mean is greater than the median. What is the likely shape of the distribution?

Accepted Answer

Skewed right

Question 7

Given the following data: 2, 4, 6, 8, 10. What is the range $$R$$?

Accepted Answer

$$R = 10 - 2 = 8$$

Question 8

A sample has mean $$\bar{x} = 50$$ and standard deviation $$s = 5. $$What is the z-score for an observation $$x = 60$$?

Accepted Answer

$$z = \frac{60 - 50}{5} = 2$$

Question 9

Which of the following best describes a resistant statistic?

Accepted Answer

A statistic that is not affected by extreme values.

Question 10

A boxplot of household incomes shows the median near the lower quartile and a long whisker on the right. What does this indicate?

Accepted Answer

The data is skewed right.

Question 11

A scatter plot of height (x) and weight (y) for 100 adults shows a strong positive linear association. Which value of the correlation coefficient $$r is $$most likely?

Accepted Answer

$$r = 0.90$$

Question 12

Given the sample data: 3, 7, 7, 8, 10, what is the mode?

Accepted Answer

7

Question 13

A researcher uses systematic sampling to select every 10th patient from a list of 500. What is the sample size if she starts at the 3rd patient?

Accepted Answer

50

Question 14

Which formula correctly calculates the sample standard deviation $$s$$ for a sample of $$n$$ values $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

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

Question 15

A cumulative frequency table shows that the cumulative frequency for the third class is 30. If the frequency for the third class is 8, what was the cumulative frequency for the second class?

Accepted Answer

22

Question 16

A sample of 8 values has $$Q_1 = 12$, Q_3$ = 20. $$What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 8$$

Question 17

A least-squares regression line is given by $$y = 2x + 5. $$What is the predicted value $$\hat{y}$$ when $$x = 4$$?

Accepted Answer

$$\hat{y} = 2 	imes 4 + 5 = 13$$

Question 18

Which of the following is an example of response bias?

Accepted Answer

Survey respondents give answers they think are socially acceptable rather than truthful.

Question 19

A sample of 10 values has $$Q_1 = 15$, Q_3$ = 25$$, and the maximum value is 40. What is the upper fence for outliers?

Accepted Answer

$$	ext{Upper fence} = Q_3$ + 1.5 	imes IQR = 25 + 1.5 	imes (25 - 15) = 40$$

MA 113: Midterm 1 Study Guide – Data Collection, Summarizing, and Exploring Data

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