##### Four Economic Problems Assignment
1. A sure inhabitants of people has a imply IQ of 100, however the variance is unknown. In a random pattern of 21 people, the pattern variance was s2 = 204. Calculate the next confidence intervals for ?2:(a) 95%(b) 99%2. In an agricultural experiment to find out the e?ects of a selected insecticide, a subject was planted with corn. Half the vegetation had been sprayed with the insecticide, and half had been unsprayed. A number of weeks later, impartial random samples of 200 sprayed vegetation and 200 unsprayed vegetation had been examined. The variety of wholesome vegetation in every pattern was as follows:Sprayed UnsprayedHealthy 131 111Unhealthy 69 89If the importance degree is about at zero.05, does the proof point out increased proportion of sprayed than of unsprayed vegetation had been wholesome? Use a one tailed check (notice - because the null is that the proportions are equal, use this info to assemble a pooled estimate of the proportion).three. In 1954, a examine of the e?ects of Salk polio vaccine on the incidence of paralytic polio in kids yielded the next information:Quantity Quantity ofInoculated Polio CasesWith Salk Vaccine 200,745 26With Placebo 201,229 71Is there a statistically vital di?erence within the proportion of polio incidence between these two teams of kids on the ? = zero.05 degree of significance?four. An power firm, pursuing the making of inexperienced gasoline, begins with biomass within the type of sucrose and converts it into gasoline utilizing catalytic reactions. At one step in a pilot level course of, the output contains carbon chains of size three. Fifteen runs with the identical catalyst produces the product volumes (liter)2.79, 2.88, 2.09, 2.32, three.51, three.31, three.17, three.622.79 , three.94, 2.34, three.62, three.22, 2.80, three.70 Whereas imply product quantity is the prime parameter, it is usually necessary to regulate variation. Conduct a check with the intent of exhibiting that the inhabitants customary deviation ? is lower than zero.eight litres (i.e. check H0 : ? ? ?zero versus HA : ? < ?zero, which is equal to (i.e. check H0 : ?2 ? ?02 versus HA : ?2 < ?02)). Use a significance degree of zero.05.