XR22-11 In the door-to-door selling of vacuum cleaners, various factors influence sales. The Birk…

XR22-11 In the door-to-door selling of
vacuum cleaners, various factors influence sales. The Birk Vacuum Cleaner
Company considers its sales pitch and overall package to be extremely
important. As a result, it often tries to think of new ways to sell its
product. Because the company’s management dreams up so many new sales pitches
each year, there is a two-stage testing process. In stage 1, a new plan is
tested with a relatively small sample. If there is sufficient evidence that the
plan increases sales, a second, considerably larger test is undertaken. The
statistical test is performed so
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XR22-11 In the door-to-door selling of
vacuum cleaners, various factors influence sales. The Birk Vacuum Cleaner
Company considers its sales pitch and overall package to be extremely
important. As a result, it often tries to think of new ways to sell its
product. Because the company’s management dreams up so many new sales pitches
each year, there is a two-stage testing process. In stage 1, a new plan is
tested with a relatively small sample. If there is sufficient evidence that the
plan increases sales, a second, considerably larger test is undertaken. The
statistical test is performed so that there is only a 5% chance of concluding
that the new pitch is successful in increasing sales when it actually does not
increase sales. In a stage 1 test to determine whether the inclusion of a
‘free’ 10-year service contract increases sales, 20 sales representatives were
selected at random from the company’s list of several thousand. The monthly
sales of 10 of these representatives were recorded for one month prior to the
use of the new sales pitch, and the monthly sales of the remaining 10
representatives were recorded for one month after its introduction. The results
are shown in the following table.

a If the sales are normally distributed,
should the company proceed to stage 2?

b If the sales are not normally
distributed, should the company proceed to stage 2?

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