Unformatted text preview: normal distributions
2
2 σ
= σ2 = σ 2
Variances are equal:
1
11
Then σ x1 − x2 = σ 2 ( + )
n1 n2
Interval Estimate with σ1 and σ2 unknown and small
sample case: x1 − x2 ± tα / 2 sx1 − x2 sx1 − x2 11
= s( + )
n1 n2
2 NOTE: Use t distribution 2
2
( n1 − 1) s1 + ( n2 − 1) s2
s=
n1 + n2 − 2
2 Slide 8 Interval Estimate of µ 1 µ 2
Example 1: Par, Inc. Par, Inc. is a manufacturer of golf equipment. Par has developed a new golf ball that has been designed to provide “extra distance.” In a test of driving distance using a mechanical driving device, a sample of Par golf balls was compared with a sample of golf balls made by Rap, Ltd., a competitor. The sample data is given below. Sample #1
Par, Inc.
Par, Sample #2
Sample
Rap, Ltd.
Rap, Sample Size n1 = 120 balls n2 = 80 balls Mean
Standard Deviation
Standard = 235 yards
x1 = 15 yards
s1 = 218 yards
x22= 20 yards
s Slide 9 Example 1: Par, Inc.
s Point Estimate of the Difference Between Two Population Means
µ1 = mean distance for the population of Par, Inc. golf balls
µ2 = mean distance for the population of Rap, Ltd. golf balls
(a) What is the point estimate of µ1 µ2? Slide 10 Example 1: Par, Inc.
(b) Compute the 95% Confidence Interval Estimate of the Difference Between Two Population Means.
s We are 95% confident that the difference between the mean driving distances of Par, Inc. balls and Rap, Ltd. balls lies in the interval of Slide 11 Example 2 : Specific Motors
Specific Motors of Detroit has developed a new
automobile known as the M car. 12 M cars and 8 J cars
(from Japan) were road tested to compare milesper
gallon (mpg) performance. The sample statistics are: Sample Size
Mean
Standard Deviation Sample #1 Sample #2 M Cars J Cars n1 = 12 cars n2 = 8 cars
x1
x2 = 29.8 mpg = 27.3 mpg s1 = 2.56 mpg s2 = 1.81 mpg Slide 12 Example 2: Specific Motors
s Point Estimate of the Difference Between Two Population Means µ1 = mean milespergallon for the population of M cars
µ2 = mean milespergallon for the population of J cars
(a) What is the point estimat...
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 Spring '08
 Priya
 Standard Deviation, Specific Motors

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