Answer:
The indicated confidence interval for the difference between the two population means is (-1.5159, 7.5159)
Step-by-step explanation:
Let the drying times of type A be the first population and the drying times of type B be the second population. Then
We have small sample sizes [tex]n_{1} = 11[/tex] and [tex]n_{2} = 9[/tex], besides [tex]\bar{x}_{1} = 71.5[/tex], [tex]s_{1} = 3.4[/tex] , [tex]\bar{x}_{2} = 68.5[/tex] and [tex]s_{2} = 3.6[/tex]. Therefore, the pooled
estimate is given by
[tex]s_{p}^{2} = \frac{(n_{1}-1)s_{1}^{2}+(n_{2}-1)s_{2}^{2}}{n_{1}+n_{2}-2} = \frac{(11-1)(3.4)^{2}+(9-1)(3.6)^{2}}{11+9-2} = 12.1822[/tex]
The 99% confidence interval for the true mean difference between the mean drying time of type A and the mean drying time of type B is given by
[tex](\bar{x}_{1}-\bar{x}_{2})\pm t_{0.01/2}s_{p}\sqrt{\frac{1}{11}+\frac{1}{9}}[/tex], i.e.,
[tex](71.5-68.5)\pm t_{0.005}(3.4903)\sqrt{\frac{1}{11}+\frac{1}{9}}[/tex]
where [tex]t_{0.005}[/tex] is the 0.5th quantile of the t distribution with (11+9-2) = 18 degrees of freedom. So
[tex]3\pm(-2.8784)(3.4903)(0.4495)[/tex], i.e.,
the indicated confidence interval for the difference between the two population means is (-1.5159, 7.5159)
