Q1, A manufacturer who produces light bulbs found that their "LED W10" light bulb's mean life expectancy is 5000 hours. Lately, this company has installed a new machine that can improve the lifespan of "LED W10" bulbs. With the new machine, it is believed that there has been an increase in the life expectancy of the "LED W10" bulbs. A sample of 36 bulbs after the improvisation showed an average life span of 5020 hours. Assume from past information that the standard deviation of the life span of the population is 40 hours and this also true for the new bulbs.

i)Using the critical value approach at 1% level of significance, test to determine if there has been an increase in the life expectancy of "LED W10" light bulbs. [6 marks]

ii)What is the p-value associated with the sample statistic?