Question

In an August 2012 Gallup survey of 905 randomly selected U.S. adults (age 18 and over), 54% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12. They also report that the standard error was 1.66%."

Question: Find a 95% confidence interval for the true proportion of adults who are dissatisfied with the quality of k-12 education. Show your work. Interpret your 95% confidence interval in context of the situation.​

Answer 1

Sure, here are the steps on how to find a 95% confidence interval for the true proportion of adults who are dissatisfied with the quality of k-12 education:

Find the sample proportion. The sample proportion is the number of people in the sample who are dissatisfied with the quality of k-12 education divided by the total number of people in the sample. In this case, the sample proportion is 54%.

Find the standard error of the sample proportion. The standard error of the sample proportion is a measure of how much the sample proportion can vary from the true proportion. In this case, the standard error of the sample proportion is 1.66%.

Find the 95% confidence interval. The 95% confidence interval is a range of values that is likely to contain the true proportion. To find the 95% confidence interval, we add and subtract 1.96 standard errors from the sample proportion. In this case, the 95% confidence interval is (52.34%, 55.66%).

Interpret the 95% confidence interval. The 95% confidence interval means that we are 95% confident that the true proportion of adults who are dissatisfied with the quality of k-12 education is within the range of values (52.34%, 55.66%).

In other words, if we were to repeat this survey many times, 95% of the time the confidence interval would contain the true proportion of adults who are dissatisfied with the quality of k-12 education.

Explanation: