Question

A recent poll found that "433 of the 1548 randomly-selected adults questioned felt that unemployment compensation should be extended an additional six months while the country is in its current economic downturn." We want to use this information to construct a 95% confidence interval to estimate the proportion of the U.S. adults who feel this way. (5 pts) Il. State the parameter our confidence interval will estimate and the point estimate. a. The first two conditions to construct a confidence interval are: random sample and the sample is less than 10% of the population (for Independence). Both are met. How can you confirm that the sampling distribution of sample proportions is approximately Normal? b. c. The resulting confidence interval is (0.257, 0.302). Interpret this in context. d. What is the margin of error to the interval from part c? What are 2 ways in which the margin of error in the above scenario could be reduced? e.

Answer 1

np 1548 x 0.280 -433.44 n(-p) 1548 x (1-0.280) 1114.56 The assumption is approximate p by a normal distribution is np 210 and n(1-p)210 withn 1548 is satisfied. c) Interpretation of confidence interval There are 95% confident that the proportion of U.S. adult who feel that unemployment compensation should be extended in additional six months while the country is in its current downturn is between 0.257 and 0.302 d) The margin oferror in part (c) is,