17.23 A cellphone technician wishes to estimate the average lifetime (in years) of a cellphone battery in the current market. In total there are 1183 different brands of cellphone battery selling in the market. He would like to have a 95% confidence interval for the population average lifetime of a cellphone battery, which extended to 3 years on both side of the sample average.

A simple random sample of 19 battery brands were taken.

The technician found the sample standard deviation is 5.78 years. Estimate the smallest total number of sample observations needed to achieve his goal.