1. Technically a population consisting of all steel plates produced by a steel industry company has an average length of 80 cm with a standard deviation of 7 cm. after 3 years the company technician doubts the hypothesis of the average length of the steel plate above. To assure the validity of the above hypothesis, a random sample of 100 units of steel plate is selected from the population and yields an average length of 83 cm. technicians believe that the standard deviation is still the same. Is there any reason to doubt the above hypothesis. Use Alfa 0.05

• Write the initial hypothesis and the alternative hypothesis

• Explain your conclusions