The mean life span of caterpillars before becoming butterflies is 4.75 months with a population standard deviation of 0.39 months. A caterpillarologist thinks the average life span of monarch...

The mean life span of caterpillars before becoming butterflies is 4.75 months with a population standard deviation of 0.39 months. A caterpillarologist thinks the average life span of monarch caterpillars is different from 4.75 months. The scientist collects a sample of 50 monarch caterpillars that have a mean life span of 4.85 months. Test the claim at α = .01. (BY HAND) SHOW WORK PLEASE.