EXAMPLE 7 Using confidence intervals to perform the t test for the slope
textms
Solution
From the table, we find that, for 99% confidence, for degrees of freedom is . So, our margin of error si
The 99% confidence interval for is then given by
We are 99% confident that the interval (−1.9448, −1.0552) captures the slope of the population regression line. That is, we are 99% confident that, for each additional year of age, the decrease in the number of text messages lies between 1.9448 and 1.0552.
The hypotheses are
No linear relationship exists between age and text messages.
A linear relationship exists between age and text messages.
The confidence interval from (a) does not contain zero, so we may conclude that a linear relationship exists between age and text messages, at level of significance .
NOW YOU CAN DO
Exercises 31–38.