AP Stats Inference for Slopes

There is a general concern about blood sugar and brain shrinkage. An investigation of the relationship between blood sugar levels and brain shrinkage for 22 observations are shown in the table above. Assuming the conditions for inference are met, calculate the Margin of Error for the slope of the regression line for brain shrinkage on blood sugar levels using 90% confidence.

• 0.1201

• 0.1259

• 10.1233

• 10.6127

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

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.

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.

What is the significance of hypothesis testing in the context of sampling distribution of slopes?

• Hypothesis testing in this context is crucial for assessing the reliability and generalizability of the relationship between variables.

• Hypothesis testing is irrelevant in this context

• Hypothesis testing is used to determine the sample size

• Hypothesis testing only applies to categorical variables

Explain the process of hypothesis testing using the sampling distribution of slopes.

• Creating a sampling distribution is not necessary for hypothesis testing

• Determining the standard deviation instead of the standard error

• The process of hypothesis testing using the sampling distribution of slopes involves calculating the regression line slope, creating a sampling distribution, determining the standard error, calculating the t-score and p-value, and comparing the p-value to the significance level.

• The process involves calculating the mode instead of the regression line slope

What are the assumptions underlying the inference made from the sampling distribution of slopes?

• Non-linearity, independence, homoscedasticity, and normality assumptions.

• Linearity, independence, heteroscedasticity, and non-normality assumptions.

• Linearity, dependence, heteroscedasticity, and normality assumptions.

• Linearity, independence, homoscedasticity, and normality assumptions.

Discuss the limitations of making inferences based on the sampling distribution of slopes.

• Discuss the assumptions of multicollinearity instead of linearity

• Discuss the assumptions of linearity, homoscedasticity, independence, normality of errors, and the impact of outliers and influential points on slope estimates.

• Assume that the errors are normally distributed

• Ignore the impact of outliers and influential points on slope estimates

Is time spent on social media related to GPA, among high school students?

• chi-square test for goodness of fit

• chi-square test for independence

• chi-square test for homogeneity

• t test for regression slope

Answer explanation

The relationship between two quantitative variables (time spent on social media and GPA) can be shown by linear regression and the associated t test.

The equation of the LSRL for the points on a scatterplot is ŷ = 5.3-0.23x. What is the residual for the point (5, 4)?

• -0.15

• 0.15

• 1

• 0.62

• 0.85