Calculate the Standardized Test Statistic You are testing the claim that the mean GPA of night students is greater the students. You sample 40 night students, and the sample mean GPA is 2.31 with a stando You sample 30 day students, and the sample mean GPA is 2.63 with a standard Calculate the test statistic, rounded to 2 decimal places. 13.353 Enter an integer or decimal number [more..] Submit Question Type here to search

Step 1 ：1. Identify sample means, sample standard deviations, and sample sizes: \(\bar{x}_{night} = 2.31, s_{night} = 0.650, n_{night} = 40 \); \(\bar{x}_{day} = 2.63, s_{day} = 0.740, n_{day} = 30 \)

Step 2 ：2. Calculate the difference in sample means: \(\bar{x}_{diff} = \bar{x}_{night} - \bar{x}_{day} = 2.31 - 2.63 = -0.32 \)

Step 3 ：3. Calculate the pooled standard error: \(SE = \sqrt{\frac{s_{night}^2}{n_{night}} + \frac{s_{day}^2}{n_{day}}}= \sqrt{\frac{0.650^2}{40} + \frac{0.740^2}{30}} = 0.173 \)

Step 4 ：4. Calculate the test statistic: \(t = \frac{\bar{x}_{diff}}{SE} = \frac{-0.32}{0.173} = -1.85 \)