Question

Question 6. An instructor is teaching three sections of the same course this term. There are, in sections 1,2 and 3 respectively, 24, 28 and 32 people. They take an SRS sample from each section and obtain the following grades and genders in brackets: Section 1 2 3 Grades 81 (Male) 42 (Male) 55 (Female) 78 (Female) 66 (Female) 78 (Male) 65 (Male) 79 (Male) 95 (Male) Part A. Build a 95% confidence interval for section 2. Part B. Build a 95% confidence interval for the average grade of the males in section 2. Part C. Build a 95% confidence interval for the average grade of the course.

Answer 1

95% confidence interval for meean is given by,

$\small C.I = \bar{x}\pm t_{0.05/2,n-1}\frac{S}{\sqrt{n}}$

A) Confidence interval for section 2,

Data : 42, 66, 79, 95

Sum = 282, Mean = 70.5, n = 4, Sd = 22.398, t^* = 3.182

  $\small C.I =70.5 \pm 3.182*\frac{22.398}{\sqrt{4}}$

$\small C.I =(34.86, 106.14)$

B) Confidence interval for grades of males of section 2,

Data : 42, 79, 95

Sum = 216, Mean = 72, n = 3, Sd = 27.185, t^* = 4.303

  

C.I = 72 = 4.303 * 27.185 3

$\small C.I =(4.46, 139.54)$

C) 95% confidence interval for grades of the course

Data : 81, 78, 65, 42, 66, 79, 95, 55, 78

Sum = 639, Mean = 71, n = 9, Sd = 15.796, t^* = 2.306

  $\small C.I =71 \pm 2.306*\frac{15.796}{\sqrt{9}}$

$\small C.I =(58.86, 83.14)$

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