Question: The significant decline of savings in the United States from the 1970s and 1980s to the 1990s and 2000s has been widely discussed by economists (money.cnn.com, June 30, 2010). According to the Bureau of Economic Analysis, the savings rate of American households, defined as a percentage of the disposable personal income, was 4.20% in 2009. The reported savings rate is not uniform across the country. A public policy institute conducts two of its own surveys to compute the savings rate in the Midwest. In the first survey, a sample of 160 households is taken and the average savings rate is found to be 4.48%. Another sample of 40 households finds an average savings rate of 4.60%. Assume that the population standard deviation is 1.4%.
In a report, use the above information to:
1. Compute the probability of obtaining a sample mean that is at least as high as the one computed in each of the two surveys.
2. Use these probabilities to decide which of the two samples is likely to be more representative of the United States as a whole.