Q1
Suppose that a large controlled experiment tests whether caffeine improves reaction times. A very large number of randomly selected participants are randomly given identical-seeming pills with varying doses of caffeine (including none) and then given tests of reaction times under the same conditions. The experiment finds a strong negative correlation between caffeine dose and reaction time. (Note that lower reaction times are better.)
Identify what can be concluded based on this information.
Ans:
There is evidence that caffeine causes lower (better) reaction times.
People with lower (better) reaction times generally choose to consume more caffeine.
Lower reaction times are associated with higher caffeine doses, but this study provides no evidence that caffeine causes lower reaction times.
There is no relationship between reaction time and caffeine.
Q2
Suppose that data collected from police reports of motor vehicle crashes show a moderate positive correlation between the speed of the motor vehicle at the time of the crash and the severity of injuries to the driver. Answer the following question based only on this information.
True or false: It can be concluded that the faster a motor vehicle is traveling at the time of a crash, the more severe the injuries to the driver are.
Q3
The least squares regression line for the cost of a diamond necklace from a department store (y, in dollars) in the year x years since 2000 is given by yˆ=1823+314x.
Interpret the y-intercept of the least squares regression line.
Ans:
The predicted cost of a diamond necklace from the department store is expected to increase $314 per year after the year 2000.
The predicted cost of a diamond necklace from the department store in the year 2000 is $1823.
The predicted cost of a diamond necklace from the department store in the year 2000 is $314.
The y-intercept should not be interpreted.
Q4
Which of the following situations would have data sets or plots that could have a regression line with a positive slope? Select all that apply.
Ans:
The cumulative number of ships launched by ship builders as a function of the number of months since the start of the year
The number of cars produced as a function of the number of days since the end of the last strike.
The total shipping orders that are backlogged as a function of the number of ships docked.
The number of backorders as a function of the number of assembly workers in a manufacturing company that makes the product.
Q5
An experiment finds that runners with the longest legs complete a mile run in less time.
Identify the relation between leg length and time of a mile run.
Ans:
Leg length and time of a mile run are positively correlated.
Leg length and time of a mile run are negatively correlated.
An increase in leg length causes a decrease in the time of a mile run.
A decrease in the time of a mile run causes a decrease in leg length.
Q6
A survey regarding truck engines found a positive correlation between the size of the engine and horsepower the engine produces. Answer the following question based only on this information.
True or false: It can be concluded that trucks with larger engines have greater horsepower.
Q7
Which of the following situations could produce data sets or plots that could have a regression line with a negative y-intercept? Select all that apply.
Ans:
The net profit of a company as a function of the number of months since it was founded, where net income is gross income minus expenses.
The number of employees of a company as a function of the number of months since it was founded.
The cost of a company’s flagship product as a function of the number of months since it was founded.
The number of franchises of a company as a function of the number of months since it was founded.
Q8
Which of the following situations could produce data sets or plots would have a regression line with a negative slope? Select all that apply.
Ans:
The number of miles a ship has traveled as a function of the number of years since it was launched.
The number of miles a ship travels each year as a function of the number of years since it was launched.
the number of times a ship needs repairs as a function of the number of years since the ship was initially launched.
the number of voyages a ship can make per year as a function of the length (in days) of each voyage.
Solution
Q1
Suppose that a large controlled experiment tests whether caffeine improves reaction times. A very large number of randomly selected participants are randomly given identical-seeming pills with varying doses of caffeine (including none) and then given tests of reaction times under the same conditions. The experiment finds a strong negative correlation between caffeine dose and reaction time. (Note that lower reaction times are better.)
Identify what can be concluded based on this information.
Ans:
There is evidence that caffeine causes lower (better) reaction times.
People with lower (better) reaction times generally choose to consume more caffeine.
Lower reaction times are associated with higher caffeine doses, but this study provides no evidence that caffeine causes lower reaction times.
There is no relationship between reaction time and caffeine.
Q2
Suppose that data collected from police reports of motor vehicle crashes show a moderate positive correlation between the speed of the motor vehicle at the time of the crash and the severity of injuries to the driver. Answer the following question based only on this information.
True or false: It can be concluded that the faster a motor vehicle is traveling at the time of a crash, the more severe the injuries to the driver are.
Ans: False…………please follow the link below to purchase all the solutions at $5
