Parincisamanufacturerofgolfequipmentparhasdevelopeda

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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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