Industrial light bulbs should have a mean life length acceptable to potential users and a…

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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

Set up a 99% upper confidence bound for the standard deviation of the lengths of life for the bulbs produced by this manufacturer. Is the true population standard deviation less than 150 hours? Why or why not?

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