The production process for engine control housing units of a particular type has recently been modified. Prior to this modification, historical data had suggested that the distribution of hole diameters for bushings on the housings was normal with a standard deviation of 0.100 mm. It is believed that the modification has not affected the shape of the distribution or the standard deviation, but that the value of the mean diameter may have changed. A sample of 40 housing units is selected and hole diameter is determined for each one, resulting in
The production process for engine control housing units of a particular type has recently been modified. Prior to this modification, historical data had suggested that the distribution of hole diameters for bushings on the housings was normal with a standard deviation of 0.100 mm. It is believed that the modification has not affected the shape of the distribution or the standard deviation, but that the value of the mean diameter may have changed. A sample of 40 housing units is selected and hole diameter is determined for each one, resulting in a sample mean diameter of 5.426 mm. Let's calculate a confidence interval for true average hole diameter using a confidence level of 90%. This requires that 100(1 − ?) = , from which ? = and z?/2 = z0.05 = 1.645 (corresponding to a cumulative z-curve area of 0.9500). The desired interval is then
| 0.100 | ||
|
With a reasonably high degree of confidence, we can say that 5.400 < ? < 5.452. This interval is rather narrow because of the small amount of variability in hole diameter (? = 0.100)
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