AP Stats Inference for Quantitative Data: Slopes

What is the sampling distribution of slopes?

• The sampling distribution of slopes is the distribution of slopes calculated from different samples of data.

• The sampling distribution of slopes is the distribution of intercepts calculated from different samples of data.

• The sampling distribution of slopes is the distribution of means calculated from different samples of data.

• The sampling distribution of slopes is the distribution of residuals calculated from different samples of data.

Explain the concept of inference in the context of sampling distribution of slopes.

• Inference involves calculating the mean of the sample slopes

• Inference is not relevant in sampling distribution of slopes

• Inference in the context of sampling distribution of slopes involves making conclusions about the population slope based on the sample slope.

• Inference is only applicable to large sample sizes

How can confidence intervals be used in inference based on the sampling distribution of slopes?

• Confidence intervals provide a range of plausible values for the population slope based on the sample data and its variability.

• Confidence intervals are calculated based on the mean of the sample, not the slope.

• Confidence intervals are used to determine the exact population slope without any margin of error.

• Confidence intervals are only applicable to categorical data, not slopes.

• A

• B

• C

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• E

Raoul performed an experiment using 16 windup rubber band single-propeller airplanes. He would up the propeller a different number of times and recorded the amount of time (in seconds) that the airplane flew for each number of rotations that the propeller was wound. Which of the following is a 95 percent confidence interval for the slope of the regression line that relates the number of rotations to the plane's flight time?

• 0.0462 ± (2.145)(0.01565)

• 0.924 ± (2.145)(0.6413)

• 0.0462 ± (2.96)(0.01565)

• 0.924 ± (2.96)(0.6413)

• 0.0462 ± (2.131)(0.01565)

What's the appropriate interpretation of the slope of the regression line?

• For every additional 0.61 hours of growth, the culture is predicted to weight 1 more gram.

• For every additional hour of growth, the culture is predicted to weigh 0.61 more grams.

• For every additional hour of growth, the logarithm of the culture's weight in grams is predicted to increase by 0.61.

• At the beginning of the experiment, the logarithm of the culture's weight in grams was approximately 0.61 ounces.

If the line of best fit shows the relationship between elevation and average annual temperature in celsius, what does the slope represent? Assume the line of best fit is represented by the equation

• For every 160 meters in elevation there's a decrease of 1 Celsius in temperature

• For every meter of elevation there's a decrease of 1 Celsius in temperature 

• For every  160 meters in elevation there's an increase of 1 Celsius in temperature

• For every 22.5 meters there's a decrease of 1/160 Celsius in temperature.

What is the meaning of the slope of the linear best-fit equation for the data?

• The predicted average life expectancy at birth in 1930 was about 62.7 years.

• The predicted average life expectancy at birth in 1930 was about 57.6 years.

• The average life expectancy at birth increases by about 6.7 each year.

• The average life expectancy at birth increases by about 0.2 each year.

• For every 160 meters in elevation there's a decrease of 1 Celsius in temperature

• For every meter of elevation there's a decrease of 1 Celsius in temperature 

• For every  160 meters in elevation there's an increase of 1 Celsius in temperature

• For every 22.5 meters there's a decrease of 1/160 Celsius in temperature.

If the line of best fit shows the relationship between elevation and average annual temperature in celsius, what does the slope represent? Assume the line of best fit is represented by the equation \(y=-\frac{1}{160}x+22.5\)

• For every 160 meters in elevation there's a decrease of 1 Celsius in temperature

• For every meter of elevation there's a decrease of 1 Celsius in temperature 

• For every  160 meters in elevation there's an increase of 1 Celsius in temperature

• For every 22.5 meters there's a decrease of 1/160 Celsius in temperature.