It has been reported that the average life for halogen lightbulbs is 4000 hours. Learning of this figure, a plant manager would like to find out whether the vibration and temperature conditions that the facility's bulbs encounter might be having an adverse effect on the service life of bulbs in her plant.

In a test involving 15 halogen bulbs installed in various locations around the plant, she finds the average life for bulbs in the sample is 3882 hours, with a standard deviation of 200 hours.

Assuming the population of halogen bulb lifetimes to be approximately normally distributed, and using the 0.025 level of significance, do the test results tend to support the manager's suspicion that adverse conditions might be detrimental to the operating lifespan of halogen lightbulbs used in her plant?