6. A university administrator asserted that upperclassmen spend more time studying than underclassmen. Construct the 95% confidence interval for the difference in mean time spent studying for upperclassmen and lowerclassmen. Upperclassmen 35 15.6 2.9 Underclassmen 35 12.3 4.1

The confidence interval formula is $\left({\overline{x}}_1-{\overline{x}}_2\right)\pm t*\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}$, where ${\overline{x}}_1 \text{and} {\overline{x}}_2$ are sample means, $s_1 \text{and} s_2$ are sample standard deviations, $n_1 \text{and} n_2$ are sample size for first and second sample, respectively. $t*$ is the critical value which depends on the confidence level and degrees of freedom.

Lets upperclassmen sample is first and underclassmen sample is 2. So the given data is ${\overline{x}}_1=15.6, {\overline{x}}_2=12.3, s_1=2.9$, $s_2=4.1$, $n_1=35 \text{and} n_2=35$.