1. **Problem statement:** We want to test if the average spelling score of girls is higher than that of boys. The population mean for boys is $\mu_0 = 75$. A sample of 144 boys has a sample mean $\bar{x} = 72$ and sample standard deviation $s = 8$. We test at significance level $\alpha = 0.05$ whether girls have a higher mean than boys. 2. **Hypotheses:** - Null hypothesis $H_0$: $\mu = 75$ (girls' mean is not higher) - Alternative hypothesis $H_a$: $\mu > 75$ (girls' mean is higher) 3. **Test statistic:** Since population standard deviation is unknown and sample size is large ($n=144$), we use the $z$-test: $$ z = \frac{\bar{x} - \mu_0}{s/\sqrt{n}} $$ 4. **Calculate test statistic:** $$ z = \frac{72 - 75}{8/\sqrt{144}} = \frac{-3}{8/12} = \frac{-3}{0.6667} = -4.5 $$ 5. **Decision rule:** For a right-tailed test at $\alpha=0.05$, the critical value is $z_{0.05} = 1.645$. If $z > 1.645$, reject $H_0$. 6. **Conclusion:** Our calculated $z = -4.5$ is much less than 1.645, so we do not reject $H_0$. There is no evidence at the 0.05 level that girls have a higher mean spelling score than boys. **Final answer:** The data does not support the claim that girls are better than boys in spelling at the 0.05 significance level.