Speeding Driver Statistics
2008
Statistics help pleeeease!?
A state highway patrol officer wishes to estimate the number of drivers that exceed the speed limit traveling the parkway.
a) How large a sample is needed in order to be 99% confidence that the sample proportion will not differ from the true proportion by more than 4%?
b) Repeat part a assuming previous studies found that 70% of drivers on this road exceed the speed limit.
a) ANSWER: SAMPLE SIZE = 1041
Why???
CHOOSING THE SAMPLE SIZE, POPULATION PROPORTION
π = POPULATION PROPORTION50 (50% – assumption)
B = SPECIFIED BOUND ON THE ERROR0.04
Level of Confidence99
‘z critical value’ from Look-up Table for 99%2.58
significant digits2
B = ‘z critical value’ * SQRT [ π * (1 - π )/n]
Algebraically solve for SAMPLE SIZE n :
n = π * (1 – π) * [ 'z critical value' / B ]^2 = 0.5 * (1 – 0.5) * [ 2.58 / 0.04 ]^2
SAMPLE SIZE = 1041
b) ANSWER: SAMPLE SIZE = 874
Why???
CHOOSING THE SAMPLE SIZE, POPULATION PROPORTION
π = POPULATION PROPORTION70 (70% – specified)
B = SPECIFIED BOUND ON THE ERROR0.04
Level of Confidence99
‘z critical value’ from Look-up Table for 99%2.58
significant digits2
B = ‘z critical value’ * SQRT [ π * (1 - π )/n]
Algebraically solve for SAMPLE SIZE n :
n = π * (1 – π) * [ 'z critical value' / B ]^2 = 0.7 * (1 – 0.7) * [ 2.58 / 0.04 ]^2
SAMPLE SIZE = 874
Depth Perception
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