6. (3 points) Two factories (X and Y] are producing light bulbs. To decide which one produces better products, a sample of 10 bulbs were collected 'om Factory X and a sample of E bulbs were obtained 'om Factory Y. It is known that the lifetiJne (in hours) of a light bulb is normally distributed. The sample mean and standard deviations of light bulbs 'om the two factories are Facto M 5117 11:10 m=8 i=l t7=l Sx=92 Sy=86 Test the hypothesis that the mean lifetime is the same between the light bulbs produced from both Factory X and Y. Use the 5 percent level of signicance