Final answer:
To calculate a 95% confidence interval for the slope of the true regression line, divide the standard deviation of the slope by the square root of the sample size to find the standard error.
Multiply the critical value by the standard error to find the margin of error. Subtract the margin of error from the estimated slope to find the lower bound of the confidence interval, and add the margin of error to find the upper bound.
Step-by-step explanation:
To calculate a 95% confidence interval for the slope of the true regression line, we need the standard error of the slope. The standard error can be found by dividing the standard deviation of the slope by the square root of the sample size. In this case, the standard deviation of the slope is 2.631 and the sample size is 73. Therefore, the standard error is 2.631 / sqrt(73) = 0.307.
To find the margin of error, we multiply the critical value (which corresponds to a 95% confidence level) by the standard error. The critical value can be found using the t-distribution table with degrees of freedom equal to the sample size minus 2. In this case, the critical value is approximately 2.000. Therefore, the margin of error is 2.000 * 0.307 = 0.614.
To calculate the confidence interval, we take the estimated slope (19.718) and subtract the margin of error to find the lower bound, and add the margin of error to find the upper bound. Therefore, the 95% confidence interval for the slope of the true regression line is [19.718 - 0.614, 19.718 + 0.614] = [19.104, 20.332].