Question 1

Why is a statistical study necessary for researching the average daily screen time of teenagers in a large country?

Accepted Answer

A statistical study would be used because surveying every member of the teenager population would be too difficult.

Question 2

A librarian randomly selects patrons who borrow videos to gather data on their opinions about borrowing methods. What is the correct description of the sample and population?

Accepted Answer

The sample consists of the patrons selected for the study who borrow videos; the population is all patrons of the library who borrow videos.

Question 3

A company divides a district into twenty regions and randomly selects two regions to survey all residents in those regions. What sampling method is used?

Accepted Answer

Cluster random sampling

Question 4

A doctor adjusts newborn weights by subtracting 0.25 kg from each measurement. Which statistic remains unchanged after the adjustment?

Accepted Answer

Interquartile range

Question 5

Based on the summary statistics and histogram for time spent looking at cell phones, and using the 1.5 × IQR rule, which statement is correct?

Accepted Answer

The median is greater than 6.865, and the distribution has exactly four outliers.

Question 6

Assume the distribution of body temperatures in a city is bell-shaped with mean $$98.3$$ and standard deviation $$0.733. $$Approximately 95% of the body temperatures lie between which two values?

Accepted Answer

$$96.834$$ and $$99.766$$

Question 7

Of all pints of blood classified as positive, what proportion is blood type A?

Accepted Answer

$$0.38$$

Question 8

Of all pints of blood classified as blood type A, what proportion is classified as positive?

Accepted Answer

$$0.76$$

Question 9

Azadeh creates a linear regression model for long-jump distance ($$y) $$and dash time ($$x$$): $$y = 313.875 - 30.805x$$ with $$r = -0.591. $$What is the correct interpretation of the correlation coefficient?

Accepted Answer

The linear relationship between dash time and long-jump distance is moderate and negative.

Question 10

What is the correct interpretation for the coefficient of determination ($$r^2) in $$Azadeh's model, where $$r = -0.591$$?

Accepted Answer

Approximately 35% of the variation in long-jump distance can be explained by the linear relationship with dash time.

Question 11

A teammate with a dash time of $$7$$ seconds had a residual of $$-6.8$$ inches. Based on the model $$y = 313.875 - 30.805x$$, what is the observed long-jump distance for this teammate?

Accepted Answer

$$98.24$$

Question 12

Wildlife biologists use chest circumference to estimate the weight of tule elk. The regression equation is: predicted weight $$= -350.3 + 3.7455 	imes ($$chest circumference). If an elk has a chest circumference of $$145.9 cm $$and an actual weight of $$204.3 kg$$, what is the residual?

Accepted Answer

$$-341.3$$

Question 13

Interpret the slope of the least-squares regression line for tule elk weight estimation: predicted weight $$= -350.3 + 3.7455 	imes ($$chest circumference).

Accepted Answer

For each additional cm in chest circumference, the predicted weight increases by $$3.7455 kg.$$

Question 14

At a school, $$25\% of $$students wear a watch, $$30\%$$ wear a bracelet, and $$60\%$$ wear neither. What is the probability that a randomly chosen student wears both a watch and a bracelet?

Accepted Answer

$$0.05$$

Question 15

Jane must get at least three out of four problems correct to get an A. If the probability she gets any problem correct is $$0.8$$, what is the probability she gets an A?

Accepted Answer

$$0.8192$$

Question 16

A researcher wants to estimate the average screen time of teenagers. Which of the following best describes a parameter in this context?

Accepted Answer

The average screen time of all teenagers in the country.

Question 17

Which of the following is an example of stratified random sampling?

Accepted Answer

Dividing a population into groups based on age and randomly sampling from each group.

Question 18

If a distribution is skewed right, which of the following is most likely true?

Accepted Answer

The mean is greater than the median.

Question 19

A histogram shows a distribution of time spent looking at cell phones. If the mean is $$6.865$$ and the median is less than the mean, what does this suggest about the shape of the distribution?

Accepted Answer

The distribution is skewed right.

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