Question

Name HYPOTHESIS TESTING AND ESTIMATION EXERCISE:-TEST In controlling the quality of a new drug, a dose of medicine is to contain an average of 250 parts per million (ppm) of a certain chemical. When the average concentration is 250 ppm, the population standard deviation of the chemical concentration is known to be 9.7 ppm. If the average concentration is below 250 ppm, the drug may be ineffective. The manufacturer wants to check whether the average concentration of the chemical in a large shipment is at least 250 ppm. A random sample of 41 bottles is tested, and the sample mean and sample standard deviation are found to be 247 ppm and 9.6 ppm, respectively. Is this evidence that the average concentration of the chemical in the shipment is less than 250 ppm? State the null and alternative hypotheses. Perform the test at the significance level of 5%. Find the critical value and the associated decision rule. Report the p-value of the test. I. 2. If the average concentration is higher than 250 ppm, the drug may cause some side effects. Considering both the potential side effects and the required effective concentration, restate the null and alternative hypotheses. Perform the test at 5%. Find the critical value and the associated decision rule. Report the p-value of the test. Find a 95% confidence interval for the average concen tration of the chemical in the entire shipment. 3.

Answer 1

here t-test is used where population standard deviation is known. also t-table is used for critical values.