Solve the following. Write complete and neat solutions in a bond paper or a clean sheet of paper. Specify the details you must do for each step. Write legibly. 1. According to the norms established for a history test, Grade 8 students should have an average of 81.7 with standard deviation of 8.5. If 100 randomly selected grade 8 students from a certain school district average 79.6 in this test, can we conclude that at 0.05 level of significance that Grade 8 students from this school district can be expected to have a different average than the norm of 81.7? 2. A psychologist believes that it will take at least an hour for certain special child to learn a task. A random sample of 30 of these children results in a mean of 50 minutes to learn a task. Should the psychologist modify her belief at 0.01 level if the population standard deviation can be assumed to be 15 minutes? 3. A company which produces batteries claims that the life expectancy of their batteries is at least 90 hours. To test the claim, a consumer interest group tested a random sample of 40 batteries. The test resulted to a mean life expectancy of 87 hours. Using a 0.05 level of significance, can it be concluded that the life expectancy of their batteries is less than 90 hours? Assume that the population standard deviation is known to be 10 hours. 4. The manager of the women's dress department of a store wants to know whether the true average number of women's dresses sold per day is 24. In a random sample of 36 days, it has been found that the average number of dresses sold is 23 with standard deviation of 7 dresses. At a 0.01 level of significance, is there sufficient evidence that the average is different from 24