2. (20 Points) To see if students tend to improve their SAT Mathematics (SAT-M)

Question

2. (20 Points) To see if students tend to improve their SAT Mathematics (SAT-M) score the second time they take the test, a random sample of 5 students who took the test twice was selected. The students received the following scores. Test First 500 530 600 440 710O Second 580 610 570 410 710 Assume that first and second SAT-M scores and their differences for the population of all students are normally distributed. (a) Perform the appropriate statistical test of hypothesis at the 5% level to determine if students tend to improve their SAT-M score the second time they take the test. Clearly, identify the hypothesis you are testing, report the value of the test statistic and the p-value or critical value that you are using to make your decision, and state your conclusion in the context of the problem. (b) Find a 95% confidence interval for 1-2 and interpret this interval.

Explanation / Answer

This is paired t-test hypothesis where we want to test whether test scores improves in second attempt

Below are the null and alternate hypothesis

As p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis.

This means there are not significant evidence to conclude that second attempt improves the test scores.

b)

Null Hypothesis Alternate Hypothesis H0: 1 - 2 = 0 Ha: 1 - 2 < 0

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.