Question

In: Statistics and Probability

In an August 2012 Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over),...

In an August 2012 Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over), 53% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12. They also report that the "margin of sampling error is plus or minus 4%."

  1. What is the best estimate of the proportion of U.S. adults who are dissatisfied with the quality of education students receive in kindergarten through grade 12?
  2. Find an interval estimate for the parameter of interest. Interpret it in terms of dissatisfaction in the quality of education students receive. Use two decimal places in your answer.
  3. Based on the interval give three (3) plausible proportions for the true proportion of U.S. adults who are dissatisfied with the quality of education students receive in kindergarten through grade 12.

Solutions

Expert Solution

a) The best estimate of the proportion of U.S. adults who are dissatisfied with the quality of education students receive in kindergarten through grade 12 is

= sample proportion

= 0.53

b) Let p denotes the true proportion of U.S. adults who are dissatisfied with the quality of education students receive in kindergarten through grade 12.

Interpretation : Out of 100 samples drawn, sample proportion will lie between (0.50, 0.56) for 95 samples.

c) Any value between confidence interval (0.50, 0.56) can be a plausible value of proportion for the true proportion of U.S. adults who are dissatisfied with the quality of education students receive in kindergarten through grade 12.

Three plausible proportions can be 0.52,0.53,0.54

orchestra answered 1 year ago
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