Answer:
(a) The best estimate of is 13.2.
(b) The margin of error is 5.30.
(c) The 95% confidence interval for the difference between two means is (7.90, 18.50).
Step-by-step explanation:
The (1 - <em>α</em>)% confidence interval for the difference between population means using a <em>t</em>-interval is:
(a)
A point estimate of a parameter (population) is a distinct value used for the estimation the parameter (population). For instance, the sample mean is a point-estimate of the population mean μ.
Similarly the point estimate of the difference between two means is:
Compute the point estimate of as follows:
Thus, the best estimate of is 13.2.
(b)
Compute the pooled variance as follows:
Compute the critical value of <em>t</em> as follows:
*Use a <em>t</em>-table.
Compute the margin of error as follows:
Thus, the margin of error is 5.30.
(c)
Compute the 95% confidence interval for the difference between two means as follows:
Thus, the 95% confidence interval for the difference between two means is (7.90, 18.50).