1. A school wants to estimate their seniors’ SAT scores. Students are grouped in
ID: 3303019 • Letter: 1
Question
1. A school wants to estimate their seniors’ SAT scores. Students are grouped into one of three categories: track A for the best students, track B for intermediate students, and the rest are in track C. The school decides to use stratified random sampling to reduce the variability in test scores. The school has 56 seniors in track A, 80 in track B, and 64 in track C. A stratified random sample of 50 seniors total is proportionally allocated across all three tracks.
a)How many seniors were sampled from each track?
b) Use the Minitab dataset TestScoresPerTrack.mtw to calculate the average test score and standard deviation for each track. (Hint: Use Stat > Basic Statistics > Display Descriptive Statistics > for Variables, select TestScores and for By variables, select Track.)
TestScores Track
765 A
682 A
687 A
691 A
732 A
749 A
746 A
716 A
708 A
735 A
735 A
653 A
787 A
781 A
690 B
619 B
619 B
583 B
639 B
723 B
721 B
593 B
736 B
691 B
695 B
686 B
580 B
596 B
572 B
702 B
578 B
735 B
692 B
607 B
611 C
570 C
534 C
567 C
534 C
533 C
491 C
524 C
593 C
600 C
607 C
442 C
552 C
549 C
562 C
544 C
c) Estimate the average test score for the population of all seniors.
d) For the mean estimate your provided in part (c), place a bound on the error of estimation.
Explanation / Answer
a) How many seniors were sampled from each track?
Answer:
From the given information, 56 seniors in track A, 80 in track B, and 64 in track C were sampled from the population.
b) Use the Minitab dataset TestScoresPerTrack.mtw to calculate the average test score and standard deviation for each track.
Answer:
The average test score and standard deviation for each track is given as below:
(Answered by using Minitab Output)
Welcome to Minitab, press F1 for help.
Descriptive Statistics: Test Score by Track
Variable Track N Mean Median TrMean StDev
Test Sco A 14 726.2 733.5 727.3 39.1
B 20 652.9 662.5 652.7 59.2
C 16 550.8 550.5 554.3 43.8
Variable Track SE Mean Minimum Maximum Q1 Q3
Test Sco A 10.4 653.0 787.0 690.0 753.0
B 13.2 572.0 736.0 593.8 700.3
C 11.0 442.0 611.0 533.3 587.3
c) Estimate the average test score for the population of all seniors.
Answer:
Descriptive Statistics: Test Score
Variable N Mean Median TrMean StDev SE Mean
Test Sco 50 640.7 629.0 642.0 84.5 11.9
Variable Minimum Maximum Q1 Q3
Test Sco 442.0 787.0 571.5 717.3
The estimate for the average test for population of all seniors is given as 640.7.
d) For the mean estimate your provided in part (c), place a bound on the error of estimation.
Answer:
The bound on the error of estimation or standard error for the mean is given as 11.9.
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