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4. According to a dietary study, high sodium intake may be related to ulcers, stomach cancer, and migraine headaches. The human requirement for salt is only 220 milligrams per day, which is surpassed in most single servings of ready-to- eat cereals. If a random sample of 20 similar servings of a certain cereal has a mean sodium content of 244 milligrams and a standard deviation of 24.5 milligrams, does this suggest at the 0.05 level of significance that the average sodium content for a single serving of such cereal is greater than 220 milligrams? Assume the distribution of sodium contents to be normal. 5. Past experience indicates that the time required for high school seniors to complete a standardized test is a normal random variable with a mean of 35 minutes. If a random sample of 20 high school seniors took an average of 33.1 minutes to complete this test with a standard deviation of 4.3 minutes, test the hypothesis, at the 0.05 level of significance, that u = 35 minutes against the alternative that u < 35 minutes. 6. An investigation of the oral status of a group of patients diagnosed with thalassemia. One of the outcome measures was the decayed, missing, filled teeth index (DMFT). In a sample of 18 patients , the mean DMFT index value was 10.3 with standard deviation of 7.3. Is this sufficient evidence to allow us to conclude that the mean DMFT index is greater than 9 in a population of similar subjects? Let a=0.1