Math 143 C/E
Probability and Statistics
Spring, 2001

Some two-sample inference procedure examples:

1. Discount Stores Corp. owns outlet A and outlet B. For the past year, outlet A has spent more dollars advertising casual slacks than outlet B. The corporation's advertising manager wants to see whether the advertising has resulted in more sales for outlet A. A random sample of 36 days at outlet A had a mean of 170 slacks sold daily. A random sample of 36 days at outlet B had a mean sales of 165 slacks. Assume that s_A = 6 and s_B = 5.
   • Construct a 90% confidence interval for the difference in means m_A - m_B.
     Answer: (2.86, 7.14)

   • Does the evidence support at the 5% significance level that outlet A has, indeed, sold more slacks?
     Answer: Yes (We can conclude this from the CI above.)

   • Does the evidence support at the 1% significance level that outlet A has, indeed, sold more slacks?
     Answer: Yes (z = 3.84, P < 0.0002).

2. An city housing official wants to know whether the average rent for an apartment in sector 1 of a city is different than the average rent in sector 2. She randomly samples apartment complexes in both sectors. In sector 1, her sample includes 10 observations, yielding a mean and standard deviation of $580 and $32 respectively. In sector 2, there are 12 observations for which the mean and standard deviation are $595 and $62.
   • Construct a 99% confidence interval for the difference in means m₂ - m₁.
     Answer: (-77.20, 47.20)

   • Does the evidence support at the 5% significance level that the average rent in the two sectors is different?
     Answer: No (t = 0.6921, df = 9, P > 0.5)