1. **State the problem:** We want to test if the mean starting salary for UG graduates is higher than that for KNUST graduates at the 5% significance level. 2. **Identify the test:** Since we have two independent samples and assume normality, we use a two-sample t-test for the difference of means. 3. **Set hypotheses:** - Null hypothesis $H_0$: $\mu_{UG} \leq \mu_{KNUST}$ - Alternative hypothesis $H_a$: $\mu_{UG} > \mu_{KNUST}$ (one-tailed test) 4. **Calculate sample statistics:** - UG data: $30, 35, 29, 37.5, 32, 40$ - KNUST data: $28.5, 38, 30.5, 26, 37, 29, 33, 32$ Calculate means: $$\bar{x}_{UG} = \frac{30 + 35 + 29 + 37.5 + 32 + 40}{6} = \frac{203.5}{6} = 33.9167$$ $$\bar{x}_{KNUST} = \frac{28.5 + 38 + 30.5 + 26 + 37 + 29 + 33 + 32}{8} = \frac{254}{8} = 31.75$$ Calculate sample variances: $$s_{UG}^2 = \frac{\sum (x_i - \bar{x}_{UG})^2}{n_{UG} - 1} = \frac{(30-33.9167)^2 + \cdots + (40-33.9167)^2}{5} = 18.87$$ $$s_{KNUST}^2 = \frac{\sum (x_i - \bar{x}_{KNUST})^2}{n_{KNUST} - 1} = \frac{(28.5-31.75)^2 + \cdots + (32-31.75)^2}{7} = 18.36$$ 5. **Calculate the test statistic:** Use the formula for unequal variances (Welch's t-test): $$t = \frac{\bar{x}_{UG} - \bar{x}_{KNUST}}{\sqrt{\frac{s_{UG}^2}{n_{UG}} + \frac{s_{KNUST}^2}{n_{KNUST}}}} = \frac{33.9167 - 31.75}{\sqrt{\frac{18.87}{6} + \frac{18.36}{8}}} = \frac{2.1667}{\sqrt{3.145 + 2.295}} = \frac{2.1667}{\sqrt{5.44}} = \frac{2.1667}{2.332} = 0.9295$$ 6. **Degrees of freedom:** $$df = \frac{\left(\frac{s_{UG}^2}{n_{UG}} + \frac{s_{KNUST}^2}{n_{KNUST}}\right)^2}{\frac{(s_{UG}^2/n_{UG})^2}{n_{UG}-1} + \frac{(s_{KNUST}^2/n_{KNUST})^2}{n_{KNUST}-1}} = \frac{(3.145 + 2.295)^2}{\frac{3.145^2}{5} + \frac{2.295^2}{7}} = \frac{5.44^2}{1.978 + 0.753} = \frac{29.6}{2.731} = 10.84$$ Approximate $df = 11$. 7. **Find critical value:** For a one-tailed test at $\alpha=0.05$ and $df=11$, $t_{critical} \approx 1.796$. 8. **Decision:** Since $t = 0.9295 < 1.796$, we fail to reject $H_0$. 9. **Conclusion:** There is not enough evidence at the 5% significance level to conclude that the mean starting salary for UG graduates is higher than that for KNUST graduates.