answer the question

21. [25 marks] A charity-based non-government organization (NGO) in a developing country buys sheets of clear glass, which they manufacture into contact lens. The contact lenses are then given away to poor people whose sight is failing. The glass sheets have to be 0.05 cm thick because thinner sheets could produce weak contact lens that break, causing permanent damage to a person's eyes. Lens made from sheets thicker than 0.05 cm are slightly more costly to make, since they use more material. The NGO takes a random sample of 100 sheets of glass from a particular supplier and finds that their mean thickness is 0.048 cm, and their standard deviation is 0.01 cm. (a) Set up and carry out a hypothesis test to decide whether the NGO should buy glass sheets from this supplier. Be sure to carefully state your null and alternate hypotheses, and make your decision based on the a=10% level of significance. Show all steps in your working and state the decision that you recommend for the NGO. You may need to use one of the following f- values or z-values: [10 marks] =T.INV.2T(0.05,99) 1.984 =ABS(NORM.S.INV(0.025)) 1.960 =T.INV.2T(0.1, 99) 1.660 =ABS(NORM.S.INV(0.05)) 1.645 =ABS(T.INV(0.1,99) 1.290 =ABS(NORM.S.INV(0.1)) 1.282