Question

what is the p - value? (round to 4 decimal places) using a significance level of 5%, what would this students conclusion be?
○ p - value = 0.05, thus there is sufficient evidence to say that night students have a lower mean gpa
than day students
○ p - value = 0.05, thus there is sufficient evidence to say that night students have a lower mean gpa
than day students
○ p - value > 0.05, thus there is insufficient evidence to say that night students have a lower mean gpa
than day students
○ p - value < 0.05, thus there is insufficient evidence to say that night students have a lower mean gpa
than day students

Explanation:

Part 1: Calculating the p - value

Step 1: Identify the test statistic and distribution

From the graph, we assume this is a one - tailed test (right or left - tailed, here it seems to be a right - tailed or left - tailed test for a mean difference). The test statistic \(z\) (or \(t\)) value can be used to find the p - value. Looking at the graph, the test statistic value is around \(z = 2.02\) (assuming it's a z - test, if it's a t - test, the process is similar but with t - distribution). For a one - tailed test, the p - value is the area to the right (or left) of the test statistic.

Step 2: Calculate the p - value

Using the standard normal distribution (if \(z = 2.02\)), the p - value for a right - tailed test is \(P(Z>2.02)\). We know that \(P(Z\leq2.02)=0.9783\) (from standard normal tables), so \(P(Z > 2.02)=1 - 0.9783 = 0.0217\). Rounding to 4 decimal places, the p - value is \(0.0217\).

Step 1: Compare p - value with significance level

The significance level \(\alpha=0.05\). We found that the p - value \(= 0.0217\), and \(0.0217<0.05\).

Step 2: Make the conclusion

When the p - value is less than the significance level, we reject the null hypothesis. The alternative hypothesis here is that night students have a lower mean GPA than day students (assuming the test is set up to test if night students have lower GPA). So, there is sufficient evidence to say that night students have a lower mean GPA than day students.

Answer:

The p - value is \(0.0217\)

Part 2: Making the conclusion