Playbill magazine reported that the mean annual household income of its readers is $120,000 (i.e., this figure is a sample mean). Assume that this mean is based upon a sample of size n = 25. Find a 90% confidence interval estimate for the population mean, under the following two conditions (the two parts are completely independent of each other):
a) The population standard deviation σ of household incomes is 20,000.
b) The population σ is not known, but the sample standard deviation s of incomes is 22,000.
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