AP Stats Inference for Slopes

Which one of the following provides evidence that a condition for regression inference has been met?

• A Normal probability plot of the values for the explanatory variable shows a roughly linear form.

• A scatterplot of the residuals against the values of the explanatory variable displays a random scattering of points about the line residuals = 0.

• The data consists of at least 30 observations.

Is there a relationship between reaction time and age? A statistics student measures the reaction time of 12 subjects by measuring how far a yardstick drops, in inches, before a subject catches it between his or her thumb and forefinger (a high number thus indicates a slow reaction time). The student plans to use linear regression to see if reaction time can be predicted by the age of the subject. Which one of the following is a correct set of hypotheses for testing the significance of this relationship?

• H₀ : β = 1, H_a: β ≠ 1, where β = the true slope of the population regression line.

• H₀ : β = 0, H_a: β ≠ 0, where β = the true slope of the population regression line.

• H₀ : ρ = 1, H_a: ρ < 1, where ρ = the true population correlation between age and reaction time.

• H₀ : ρ = 0, H_a: ρ < 0, where ρ = the true population correlation between age and reaction time.

Is there a relationship between reaction time and age? A statistics student measures the reaction time of 12 subjects by measuring how far a yardstick drops, in inches, before a subject catches it between his or her thumb and forefinger (a high number thus indicates a slow reaction time). The student plans to use linear regression to see if reaction time can be predicted by the age of the subject. Output from a computer regression analysis is given below. The equation of the least-squares regression line is

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Is there a relationship between reaction time and age? A statistics student measures the reaction time of 12 subjects by measuring how far a yardstick drops, in inches, before a subject catches it between his or her thumb and forefinger (a high number thus indicates a slow reaction time). The student plans to use linear regression to see if reaction time can be predicted by the age of the subject. Output from a computer regression analysis is given. Which of the following is the correct decision for the test of H₀ : β = 0 versus H_a : β ≠ 0 at the α = 0.05 level? Assume all conditions for inference have been met.

• Because the P-value is less than the significance level, we reject H₀. There is strong evidence of a linear relationship between age and reaction time.

• Because the P-value is 0.365, which is more than a 5% significance level, we fail to reject H₀. We do not have evidence of a linear relationship between age and reaction time.

• Because the P-value is less than the significance level, we fail to reject H₀. We do not have evidence of a linear relationship between age and reaction time.

• Because the P-value is 0.365, which is more than a 5% significance level, we reject H₀. There is strong evidence of a linear relationship between age and reaction time.

Sarah runs an ice cream stand at a beach resort, and she is interested in predicting each day’s ice cream sales (in dollars) from the air temperature at 8:00 am (in degrees Fahrenheit). She randomly selects 12 days during the previous summer and calculates a least squares regression of sales on air temperature. A computer output of her regression is given below. Which one of the following is a correct interpretation of the number 1.646?

• For each 1° increase in air temperature, ice cream sales are predicted to increase, on average, by $1.65

• For samples of size 12, the typical deviation of a sample slope from the population (true) slope is estimated to be 1.646

• For this sample, the typical distance between an observed temperature and the mean temperature is 1.646

Forestry managers keep records giving the number of board feet B (in hundreds of board feet) of lumber produced by harvesting white pine trees with diameter D (in inches), so that they can predict the amount of lumber that can be harvested from a tree from its diameter. A scatterplot of B vs. D shows a strongly curved shape, but taking the natural logarithm of both variables produces a linear scatterplot. This computer output below is for a least squares linear regression of vs for 9 white pine trees. Which one of the following is a correct regression equation for these data?

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With practice, people become faster at solving a certain type of mathematical puzzle. Fourteen college students were allowed to practice completing a certain type of mathematical puzzle for different amounts of time. Afterwards, each student’s completion time on a new puzzle was measured. The Residual plot for regression of Completion Time on Practice Time is shown below. Which of the following is correct?

• There is a no relationship between Practice Time and Puzzle Completion Time.

• This regression equation would likely overestimate the Puzzle Completion Time for 175 minutes of practice time.

• There is a non-linear relationship between Practice Time and Puzzle Completion Time.

What is the regression estimated regression equation

• expected sale price = 16.470 -0.059 mileage

• expected mileage = 16.470 -0.059 sale price

• y = 16.470 - 0.059 x

• x = 16.470 - 0.059 y

What is the the result of the test Ho: b₁ = 0 H₁ : b₁ ≠ 0 at the significance level of 5%?

• Reject the null hypothesis, because the p value i=0 is less than the significance level.

• Accept the null hypothesis, because the p value i=0 is less than the significance level.

• Accept the null hypothesis, because the t-stat = 17.359 is larger than 2.

• There is not enough information.