Question

In: Statistics and Probability

AT coaching: A sample of 10 students took a class designed to improve their SAT math...

AT coaching: A sample of

10

students took a class designed to improve their SAT math scores. Following are their scores before and after the class.

Before

After

451

454

453

463

491

511

526

529

473

493

440

466

481

482

459

455

399

404

383

420

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Part 1 of 2

(a) Construct a

95%

confidence interval for the mean increase in scores after the class. Let

d

represent the SAT score after taking the class minus the SAT score before. Use tables to find the critical value and round the answers to at least one decimal place.

A

95%

confidence interval for the mean increase in scores after the class is

<<μd

Expert Solution

Mean and standard deviation was calculated using MS Excel.

Step 1: Find α/2
Level of Confidence = 95%
α = 100% - (Level of Confidence) = 5%
α/2 = 2.5% = 0.025

Step 2: Find t_α/2
Calculate t_α/2 by using t-distribution with degrees of freedom (DF) as n - 1 = 10 - 1 = 9 and α/2 = 0.025 as right-tailed area and left-tailed area.

t_α/2 = 2.262

Step 3: Calculate 95% Confidence Interval

Lower Bound = d̄ - t_α/2•(s_d/√n) = 12.1 - (2.26211)(13.0848/√10) = 2.74
Upper Bound = d̄ + t_α/2•(s_d/√n) = 12.1 + (2.26211)(13.0848/√10) = 21.46
Confidence Interval = (2.74, 21.46)

95% confidence interval for the mean increase in scores after the class is: 2.74 < μ_d < 21.46

orchestra answered 2 years ago

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