Is July Really Rainier Than August in Tucson? A Statistical Analysis
a. The hypothesis appropriate to your friend's suspicion is:
H0: The mean rainfall total in July is equal to or less than the mean rainfall total in August. Ha: The mean rainfall total in July is greater than the mean rainfall total in August.
Population parameters: μ_July = population mean rainfall total in July μ_August = population mean rainfall total in August
b. In this case, we will use a one-tailed, paired samples t-test to compare the means of the two months. We will use a paired samples t-test because we are comparing the means of the same sample (Tucson's rainfall) at two different times (July and August). We will use a one-tailed test because we are testing if July has a greater mean rainfall total than August.
Explanation: A paired samples t-test is appropriate because we are comparing the means of the same sample at two different times. A one-tailed test is appropriate because we have a specific direction in mind (July having a greater mean rainfall total than August).
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