Confidence Intervals

  1) The collapse of the housing bubble in 2008 saw housing prices in the largest cities losing a third of their value, the stock market nearly collapsed, and unemployment doubled. Yet, the story of the recession isn't necessarily one of loss so much as it is of increasing income inequality. While families hovering around the average net worth lost 36% in the decade spanning from 2003 to 2013, people in the top 95th percentile actually gained 14% in the same tumultuous period. In one large community, a random sample of 55 homes found an average loss in home value of $29, 675 from 2003 to 2013 with a standard deviation of approximately $4,000. (8 pts) a) Use the TInterval command in your calculator to find a 98% confidence interval for the mean loss in home value in this community. To receive credit, write the command and the values you entered.   b) Interpret the interval you found in part (a).   c) Use the interval you found in part (a) to find the margin of error associated with this confidence interval.   d) A government official claims that in this community the mean loss in home value is more than $28,000, does your interval contradict this claim? Explain.     2) In October 2019, Gallup asked a random sample of 1,506 Americans which of two approaches to punishing murder they thought was better, the death penalty or life without the possibility of parole. For the first time since Gallup began asking the question in 1985, a majority of Americans, 60% (904 out of the 1506 Americans sampled), now say life imprisonment is a better approach for punishing murder. 36% favored the death penalty. (6 pts) a) Use the 1-PropZInt command in your calculator to find a 95% confidence interval for the proportion of Americans that now believe life imprisonment is a better approach for punishing murder. To receive credit, write the command and the values you entered.   b) Interpret your interval above in the context of this problem.   c) A local official claims that 65% of Americans believe life imprisonment is a better approach for punishing murder. Does your confidence interval contradict this claim? Explain.     3) Minnesota Public Radio wants to duplicate a survey conducted in 2016 that found that 65% of adults living in Minnesota felt that the country was going in the wrong direction. How many people would need to be surveyed for a 90% confidence interval to ensure the margin of error would be 3%? To receive credit, write the formula and the values you entered. Be sure to round properly. (4 pts)     4) Suppose the problem above (#3) included no previous survey information and instead said: Minnesota Public Radio is planning to conduct a survey to find the proportion of adults living in Minnesota that feel the country was going in the wrong direction. How many people would need to be surveyed for a 90% confidence interval to ensure the margin of error would be 3%? How will your calculation change? Solve this alternate version of the problem. To receive credit, write the formula and the values you entered. Be sure to round properly. (4 pts)