Posted: February 5th, 2019
Four Economic Problems Assignment
1. A certain population of individuals has a mean IQ of 100, but the variance is unknown. In a random sample of 21 individuals, the sample variance was s2 = 204. Calculate the following confidence intervals for ?2:(a) 95%(b) 99%2. In an agricultural experiment to determine the e?ects of a particular insecticide, a field was planted with corn. Half the plants were sprayed with the insecticide, and half were unsprayed. Several weeks later, independent random samples of 200 sprayed plants and 200 unsprayed plants were examined. The number of healthy plants in each sample was as follows:Sprayed UnsprayedHealthy 131 111Unhealthy 69 89If the significance level is set at 0.05, does the evidence indicate that a higher proportion of sprayed than of unsprayed plants were healthy? Use a one tailed test (note – since the null is that the proportions are equal, use this information to construct a pooled estimate of the proportion).3. In 1954, a study of the e?ects of Salk polio vaccine on the incidence of paralytic polio in children yielded the following data:Number Number ofInoculated Polio CasesWith Salk Vaccine 200,745 26With Placebo 201,229 71Is there a statistically significant di?erence in the proportion of polio incidence between these two groups of children at the ? = 0.05 level of significance?4. An energy company, pursuing the making of green gasoline, starts with biomass in the form of sucrose and converts it into gasoline using catalytic reactions. At one step in a pilot point process, the output includes carbon chains of length 3. Fifteen runs with the same catalyst produces the product volumes (liter)2.79, 2.88, 2.09, 2.32, 3.51, 3.31, 3.17, 3.622.79 , 3.94, 2.34, 3.62, 3.22, 2.80, 3.70 While mean product volume is the prime parameter, it is also important to control variation. Conduct a test with the intent of showing that the population standard deviation ? is less than 0.8 litres (i.e. test H0 : ? ? ?0 versus HA : ? < ?0, which is equivalent to (i.e. test H0 : ?2 ? ?02 versus HA : ?2 < ?02)). Use a significance level of 0.05.
