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. 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%.
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.