Step 1 :Define the null and alternative hypothesis: \(H_{0}: \mu \geq 3.5\) and \(H_{1}: \mu<3.5\). This is a left-tailed test.
Step 2 :Given a sample of 55 students, a sample mean of 3.47, and a standard deviation of 0.07.
Step 3 :Calculate the test statistic using the formula: \((sample \: mean - population \: mean) / (standard \: deviation / \sqrt{sample \: size})\). The test statistic is approximately -3.18.
Step 4 :Calculate the p-value using a z-table or a statistical software. The p-value is approximately 0.00074.
Step 5 :Compare the p-value with the significance level. Since the p-value (0.00074) is less than the significance level (0.025), we reject the null hypothesis.
Step 6 :Final Answer: We reject the null hypothesis. The mean GPA of night students is less than 3.5. \(\boxed{Reject \: the \: null \: hypothesis}\).