Statistics and Probability - Interpreting Categorical and Quantitative Data
PrintInterpreting Data covers summarizing data with plots, computing measures of center and spread, and fitting linear models to scatter plots. Two-way frequency tables add categorical data analysis. Content spans Algebra 1 and Statistics courses.
Example Problems
What is the critical value for constructing a 90% confidence interval?
A fishery biologist recorded the length of trout, in centimeters, and their weight, in grams.
After plotting her results, the biologist noticed that the relationship between the two variables was fairly linear, so she used the data to calculate the following least squares regression equation for predicting weight, in grams, from length, in centimeters:
What is the residual for a trout that is long and weighs ?
After plotting her results, the biologist noticed that the relationship between the two variables was fairly linear, so she used the data to calculate the following least squares regression equation for predicting weight, in grams, from length, in centimeters:
What is the residual for a trout that is long and weighs ?
Isabella is studying the relationship between daily study hours and exam score. She records data for a random sample of 22 students. Here is computer output from a least-squares regression analysis on her sample:
Assume that all conditions for inference have been met.
Write the expression for a 99% confidence interval for the slope of the least squares regression line.
| Predictor | Coef | SE Coef | T | P |
|---|---|---|---|---|
| Constant | 52.30 | 5.05 | 10.36 | 0.00 |
| Study hours | 4.52 | 1.05 | 4.30 | 0.00 |
Assume that all conditions for inference have been met.
Write the expression for a 99% confidence interval for the slope of the least squares regression line.
Identify any outliers from the following table:
| Data Value |
|---|
| 84 |
| 7 |
| 9 |
| 8 |
Jamal collected data on vehicle engine displacement (in liters) and CO2 emissions (in grams per kilometer) for a random sample of 41 car models. Here is computer output from a least-squares regression analysis on his sample:
S = 48.60 R-sq = 69.5%
Assume that all conditions for inference have been met.
Write the expression for a 95% confidence interval for the slope of the least squares regression line.
| Predictor | Coef | SE Coef | T | P |
|---|---|---|---|---|
| Constant | 74.20 | 22.80 | 3.26 | 0.00 |
| Displacement | 68.30 | 11.90 | 5.74 | 0.00 |
S = 48.60 R-sq = 69.5%
Assume that all conditions for inference have been met.
Write the expression for a 95% confidence interval for the slope of the least squares regression line.

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