In: Math
In an article in the Journal of Marketing, Bayus
studied the differences between "early replacement buyers” and
"late replacement buyers” in making consumer durable good
replacement purchases. Early replacement buyers are consumers who
replace a product during the early part of its lifetime, while late
replacement buyers make replacement purchases late in the product’s
lifetime. In particular, Bayus studied automobile replacement
purchases. Consumers who traded in cars with ages of zero to three
years and mileages of no more than 35,000 miles were classified as
early replacement buyers. Consumers who traded in cars with ages of
seven or more years and mileages of more than 73,000 miles were
classified as late replacement buyers. Bayus compared the two
groups of buyers with respect to demographic variables such as
income, education, age, and so forth. He also compared the two
groups with respect to the amount of search activity in the
replacement purchase process. Variables compared included the
number of dealers visited, the time spent gathering information,
and the time spent visiting dealers.
(a) Suppose that a random sample of 796 early replacement buyers yields a mean number of dealers visited of x¯x¯ = 3.1, and assume that σ equals .77. Calculate a 99 percent confidence interval for the population mean number of dealers visited by early replacement buyers. (Round your answers to 3 decimal places.)
The 99 percent confidence interval is
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].
(b) Suppose that a random sample of 496 late
replacement buyers yields a mean number of dealers visited of x¯x¯
= 4.8, and assume that σ equals .64. Calculate a 99
percent confidence interval for the population mean number of
dealers visited by late replacement buyers. (Round your
answers to 3 decimal places.)
The 99 percent confidence interval is
[,
].
(c) Use the confidence intervals you computed
in parts a and b to compare the mean number of
dealers visited by early replacement buyers with the mean number of
dealers visited by late replacement buyers. How do the means
compare?