3.1 The grade point averages (GPA) for 12 randomly selected college students are

Question

3.1 The grade point averages (GPA) for 12 randomly selected college students are shown on the right. Complete parts (a) through (c) 2.3 below. 1.80.6 4.0 Assume the population is normally distributed. 2.4 1.4 3.6 0.22.3 3.4 0.2 3.4 (a) Find the sample mean. x=I(Round to two decimal places as needed.) (b) Find the sample standard deviation. s=](Round to two decimal places as needed.) (c) Construct a 95% confidence interval for the population mean . A 95% confidence interval for the population mean is (). (Round to two decimal places as needed.) Enter your answer in each of the answer boxes.

Explanation / Answer

The scores are 2.3, 3.1, 2.8, 1.8, 0.6, 4.0, 2.4, 1.4, 3.6, 0.2, 2.3, 3.4.

x' = (2.3 + 3.1 + 2.8 + 1.8 + 0.6 + 4.0 + 2.4 + 1.4 + 3.6 + 0.2 + 2.3 + 3.4) / 12

= 2.325 = 2.33.

s2 = (2.3*2.3 + 3.1*3.1 + 2.8*2.8 + 1.8*1.8 + 0.6*0.6 + 4.0*4.0 + 2.4*2.4 + 1.4*1.4 + 3.6*3.6 + 0.2*0.2 + 2.3*2.3 + 3.4*3.4)/11 - (2.325 * 2.325) * 12/11 = 1.3675.

s = 1.3675 = 1.17.

z for 95% = 1.96.

LCL = 2.325 - 1.17 * 1.96 / 12 = 1.6630.

UCL = 2.325 + 1.17 * 1.96 / 12 = 2.9870.

The confidence interval is (1.66, 2.99).

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

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