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					Example 8.6


Confidence Interval for the Difference
         Between Means
Background Information
   The SureStep Company manufactures high-quality
    treadmills for use in exercise clubs.

   SureSteps currently purchases its motors for these
    treadmills from supplier A.

   However, it is considering a change to supplier B,
    which offers a slightly lower cost. The only question is
    whether supplier B’s motors are as reliable as
    supplier A’s.


     8.1 | 8.2 | 8.3 | 8.4 | 8.5 | 8.7 | 8.8 | 8.9 | 8.10 | 8.11 | 8.12 | 8.13 | 8.14
Background Information --
continued
   To check this SureStep installs motors from supplier
    A on 30 of its treadmills and motors from supplier B
    on another 30 of its treadmills.

   It then runs these treadmills under typical conditions
    and, for each treadmill, records the number of hours
    until the motor fails.

   What can SureStep conclude?




     8.1 | 8.2 | 8.3 | 8.4 | 8.5 | 8.7 | 8.8 | 8.9 | 8.10 | 8.11 | 8.12 | 8.13 | 8.14
      MOTORS.XLS
   The data from the experiment appears in this file.
    Here is a portion of that data.




     8.1 | 8.2 | 8.3 | 8.4 | 8.5 | 8.7 | 8.8 | 8.9 | 8.10 | 8.11 | 8.12 | 8.13 | 8.14
Boxplots
   In any comparison problem it is a good idea to look
    initially at side-by-side boxplots of the two samples.




     8.1 | 8.2 | 8.3 | 8.4 | 8.5 | 8.7 | 8.8 | 8.9 | 8.10 | 8.11 | 8.12 | 8.13 | 8.14
Boxplots -- continued
   The boxplots show
    – the distribution of times until failure are skewed to the right
      for each supplier

    – the mean for supplier A is somewhat greater than the mean
      for supplier B

    – there are several mild outliers

   There seems to be little doubt that supplier A’s
    motors will last longer on average than supplier B’s -
    or is there?

     8.1 | 8.2 | 8.3 | 8.4 | 8.5 | 8.7 | 8.8 | 8.9 | 8.10 | 8.11 | 8.12 | 8.13 | 8.14
Confidence Interval
   A confidence interval for the mean difference allows
    us to see whether the differences apparent in the
    boxplots can be generalized to all motors from the
    two suppliers.

   We find this confidence interval by using StatPro
    Two-Sample procedure.

   It shows that the sample means differ by
    approximately 93 hours and that the sample standard
    deviations are of roughly the same magnitude.

     8.1 | 8.2 | 8.3 | 8.4 | 8.5 | 8.7 | 8.8 | 8.9 | 8.10 | 8.11 | 8.12 | 8.13 | 8.14
Confidence Interval -- continued
   The difference between sample means is 93.133
    hours, the pooled estimate of the common population
    standard deviation is 272.196 hours, the standard
    error of the sample mean difference is 70.281 hours;
    these values lead to the following 95% confidence
    interval for the mean difference: 47.549 to 233.815.

   Not only is this interval wide but it ranges from a
    negative value to a positive value.

   If SureStep has to guess they would say that supplier
    A’s motors lasted longer, but because of the negative
    number there is still a possibility that the opposite is
    true.
     8.1 | 8.2 | 8.3 | 8.4 | 8.5 | 8.7 | 8.8 | 8.9 | 8.10 | 8.11 | 8.12 | 8.13 | 8.14

				
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posted:6/23/2011
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