Step 1 :Define the null hypothesis as \(H_{0}: \mu=3\) and the alternative hypothesis as \(H_{1}: \mu>3\).
Step 2 :The given sample size is 40, the sample mean is 3.03, and the sample standard deviation is 0.14.
Step 3 :Calculate the test statistic using the formula \(Z = \frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt{n}}}\), where \(\bar{X}\) is the sample mean, \(\mu\) is the population mean, \(\sigma\) is the standard deviation, and \(n\) is the sample size. The calculated test statistic is approximately 1.36.
Step 4 :Calculate the p-value, which is the probability of observing a result as extreme as the test statistic, assuming the null hypothesis is true. The calculated p-value is approximately 0.088.
Step 5 :Compare the p-value with the significance level (0.01). Since the p-value is greater than the significance level, we fail to reject the null hypothesis.
Step 6 :\(\boxed{\text{Final Answer: We fail to reject the null hypothesis. The data does not provide strong evidence to support the claim that the mean GPA of night students is larger than 3.}}\)