The mean time between failures for a Telektronic Company radio used in light aircraft is 420 hours. After 15 new radios were modified in an attempt to improve reliability, tests were conducted to measure the times between failures. The 15 radios had a mean time between failures of 442 hours with a standard deviation of 44.0 hours. Use a 0.05 significance level to test the claim that modified radios have a mean time between failures that is greater than 420 hours. Does it appear that the modifications improved reliability?