Industrial light bulbs should have a mean life length acceptable to potential users and a relatively small variation in life length. If some bulbs fail too early in their life, users become annoyed and are likely to switch to bulbs produced by a different manufacturer. Large variations above the mean reduce replacement sales; in general, variation in life lengths disrupts the user’s replacement schedules. A random sample of 20 bulbs produced by a particular manufacturer produced the following lengths of life (in hours): 2100, 2302, 1951, 2067, 2415, 1883, 2101, 2146, 2278, 2019, 1924, 2183, 2077, 2392, 2286, 2501, 1946, 2161, 2253, 1827. (a) Find a 99% confidence interval for the standard deviation of the lengths of life for the bulbs produced by this manufacturer. (b) Is the true population standard deviation possibly less than 150 hours? Why or why not?
Industrial light bulbs should have a mean life length acceptable to potential users and a relatively
small variation in life length. If some bulbs fail too early in their life, users become annoyed and are
likely to switch to bulbs produced by a different manufacturer. Large variations above the mean
reduce replacement sales; in general, variation in life lengths disrupts the user’s replacement
schedules. A random sample of 20 bulbs produced by a particular manufacturer produced the
following lengths of life (in hours):
2100, 2302, 1951, 2067, 2415, 1883, 2101, 2146, 2278, 2019,
1924, 2183, 2077, 2392, 2286, 2501, 1946, 2161, 2253, 1827.
(a) Find a 99% confidence interval for the standard deviation of the lengths of life for the bulbs
produced by this manufacturer.
(b) Is the true population standard deviation possibly less than 150 hours? Why or why not?
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