Question 1

A study of the effect of abortions on the health of subsequent children was conducted by obtaining names of women who had abortions, finding those who bore a child within five years, and then examining hospital records for the health of the newborn child. What type of study is this, and why?

Accepted Answer

An observational study, because the researchers did not assign treatments but only observed outcomes.

Question 2

A social media researcher wants to study the average daily screen time of teenagers in a large country. Why is a statistical study necessary for this research?

Accepted Answer

A statistical study is used because surveying every teenager would be too difficult.

Question 3

A company divides a district into 20 regions, randomly selects 2 regions, and surveys all residents in those regions. What sampling method is this?

Accepted Answer

Cluster random sampling

Question 4

Which of the following can be used to show a cause-and-effect relationship between two variables?

Accepted Answer

A controlled experiment

Question 5

A doctor records the weights of newborn babies using a scale that adds 0.25 kg to each measurement. After correcting the error by subtracting 0.25 kg from each value, which statistic remains unchanged?

Accepted Answer

Interquartile range

Question 6

Refer to the first histogram (students finishing a game). Which statement best describes the distribution?

Accepted Answer

The distribution is skewed to the right.

Question 7

Refer to the second histogram (dentist waiting times). Which value could be the median waiting time, in minutes?

Accepted Answer

$$7.25$$

Question 8

A telemarketing firm dials 100 random numbers and finds 43 are unlisted. If 52% of all phones are unlisted, what is the number 43 in this context?

Accepted Answer

A statistic

Question 9

The heights of adult women are approximately normally distributed with mean $$65$$ inches and standard deviation $$2$$ inches. What is the height at the 99th percentile?

Accepted Answer

$$70$$

Question 10

Assume body temperatures are bell-shaped with mean $$98.3$$ and standard deviation $$0.733. $$Approximately 95% of body temperatures lie between which two values?

Accepted Answer

$$96.834$$ and $$99.766$$

Question 11

Based on the blood drive table, of all pints of blood classified as positive, what proportion is blood type A?

Accepted Answer

$$0.38$$

Question 12

Joe and Matthew visit a bookstore. The probability that Joe buys no books is $$0.50$$ and for Matthew it is $$0.25. $$What is the probability that neither buys a book?

Accepted Answer

$$0.0625$$

Question 13

A magazine has $$1,620,000$$ subscribers: $$640,000$$ women (30% read ads) and $$980,000$$ men (50% read ads). In a random sample of $$100$$ subscribers, what is the expected number who read the ads?

Accepted Answer

$$42$$

Question 14

A manufacturer claims $$98\%$$ reliability for its lightbulbs. In a random sample of $$1,000$$ bulbs, what is the expected number of nondefective bulbs?

Accepted Answer

$$980$$

Question 15

A nonprofit sells $$1,000$$ raffle tickets at $$\1$ each. One ticket wins $$\$$50. $$The expected value for the net gain per ticket is $$-\0.95$. What does this mean?

Accepted Answer

The ticket owners lose an average of $$\0.95$ per ticket.

Question 16

A company blood drive collected 42 pints of blood. Of all pints classified as blood type A, what proportion is classified as positive?

Accepted Answer

$$0.76$$

Question 17

A scatterplot shows a linear relationship between two variables. The least squares regression line is $$\hat{y} = 1.3 + 0.73x. $$What is the residual for the point $$(4, 7)$$?

Accepted Answer

$$2.78$$

Question 18

A biologist fits the model $$\hat{y} = 25.2 + 3.3x$$ for the relationship between cricket chirps per minute ($$x) $$and temperature ($$y in$$ °F). What is the estimated increase in temperature for an increase of 5 chirps per minute?

Accepted Answer

$$8.25$$

Question 19

A regression model for long-jump distance ($$y) $$and dash time ($$x) is$$ $$y = 313.875 - 30.805x$$ with $$r = -0.591. $$Which 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 20

A regression model for long-jump distance ($$y) $$and dash time ($$x) is$$ $$y = 313.875 - 30.805x$$ with $$r = -0.591. $$What does the coefficient of determination ($$r^2) $$tell us?

Accepted Answer

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

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