Question 1

Which of the following correctly describes the interval notation for all real numbers between 10 and 50, including both endpoints?

Accepted Answer

$$ [10, 50] $$

Question 2

Given the interval $$ [20, 90] $$, what is the center (midpoint) of the interval?

Accepted Answer

$$ 55 $$

Question 3

An interval is written as $$ 150 \pm 30 . $$What is the width of this interval?

Accepted Answer

$$ 60 $$

Question 4

If an interval has a center of $$ 50 $$ and a width of $$ 40 $$, what is the margin of error?

Accepted Answer

$$ 20 $$

Question 5

Which of the following statements about rational and irrational numbers is TRUE?

Accepted Answer

A rational number either terminates or repeats in decimal form.

Question 6

The interval $$ [a, b] $$ has a width of $$ w . $$Which formula correctly expresses the width?

Accepted Answer

$$ w = b - a $$

Question 7

Suppose an interval is written as $$ c \pm m $$, where $$ c  is $$the center and $$ m  is $$the margin of error. What are the left and right endpoints?

Accepted Answer

Left endpoint: $$ c - m $$, Right endpoint: $$ c + m $$

Question 8

A confidence interval for the mean blood pressure in a population is given as $$ 120 \pm 8 . $$What is the interval in notation, assuming both endpoints are included?

Accepted Answer

$$ [112, 128] $$

Question 9

If the interval $$ [a, b] $$ has a center $$ c $$, which formula correctly calculates $$ c $$?

Accepted Answer

$$ c = \frac{a + b}{2} $$

Question 10

A statistical interval is written as $$ 14 \pm 10 . $$What is the width of the interval?

Accepted Answer

$$ 20 $$

Question 11

Given the interval $$ [120, 180] $$, what is the margin of error?

Accepted Answer

$$ 60 $$

Question 12

If an interval is written as $$ center \pm margin \ of \ error $$, and the width is $$ 50 $$ and the margin of error is $$ 2s $$, what is the value of $$ s $$?

Accepted Answer

$$ 12.5 $$

Question 13

Which of the following best describes the margin of error in a statistical interval?

Accepted Answer

It is half the width of the interval.

Question 14

A researcher reports the interval $$ [30, 70] $$ for the average test score. What is the center and margin of error?

Accepted Answer

Center: $$ 50 $$, Margin of error: $$ 20 $$

Question 15

Which of the following intervals includes both endpoints?

Accepted Answer

$$ [5, 10] $$

Question 16

If the interval $$ [a, b]  is $$written as $$ c \pm m $$, what is the relationship between the width and the margin of error?

Accepted Answer

Width is twice the margin of error.

Question 17

A medical study reports the interval $$ [80, 120] $$ for cholesterol levels. What is the center and width of the interval?

Accepted Answer

Center: $$ 100 $$, Width: $$ 40 $$

Question 18

Which of the following is NOT a property of a bounded interval?

Accepted Answer

The left endpoint can be greater than the right endpoint.

Question 19

A statistical interval is given as $$ [4, 24] . $$Express this interval in the form $$ center \pm margin \ of \ error .$$

Accepted Answer

$$ 14 \pm 10 $$

Question 20

If the interval $$ [a, b] $$ has a width of $$ w $$ and center $$ c $$, which formula gives the margin of error?

Accepted Answer

$$ m = \frac{w}{2} $$

Intervals and Their Properties in Statistics

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