Final answer:
To construct a confidence interval for μd, the mean of the differences for a population of paired data, the formula (x - t * Sd / sqrt(n), x + t * Sd / sqrt(n)) can be used, where x is the sample mean, Sd is the sample standard deviation, n is the sample size, and t is the critical value for the desired confidence level and degrees of freedom. Plugging in the given values, we can determine a 90 percent confidence interval for μd. The answer is (-5.086, 11.336)
Step-by-step explanation:
To construct a confidence interval for the mean of the differences for a population of paired data, we can use the sample mean and standard deviation. In this case, the sample mean (x) is 3.125, the sample standard deviation (Sd) is 2.911, and the sample size (n) is 8. To determine a 90 percent confidence interval for μd, we can use the formula:
(x - t * Sd / sqrt(n), x + t * Sd / sqrt(n))
Where t is the critical value for the desired confidence level and degrees of freedom. For a 90 percent confidence level and 8 degrees of freedom, the critical value is approximately 1.860. Plugging in the values, we get:
(3.125 - 1.860 * 2.911 / sqrt(8), 3.125 + 1.860 * 2.911 / sqrt(8))
Simplifying the equation gives:
(-5.086, 11.336)