In an effort to reduce billing time an lawn-care firm replaces their old billing system with a new one that has promised to reduce billing time by at least 5 days (compared to the system the lawn-care firm is currently using). In a sample of 135 customers under the previous system, the average payment time was 26 days with a standard deviation of 12 days. In a sample of 85 customers under the new system, the average payment time is 18 days with a standard deviation of 10 days. Since the new system is much more expensive to operate, the lawn-care firm will only continue with the new system if they can be very sure that it reduced billing time by at least 5 days. At the 1% level of significance, does it appear that the new billing system has lowered the billing time by at least 5 days?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
In an effort to reduce billing time an lawn-care firm replaces their old billing system with a new one
that has promised to reduce billing time by at least 5 days (compared to the system the lawn-care firm
is currently using). In a sample of 135 customers under the previous system, the average payment time
was 26 days with a standard deviation of 12 days. In a sample of 85 customers under the new system,
the average payment time is 18 days with a standard deviation of 10 days. Since the new system is
much more expensive to operate, the lawn-care firm will only continue with the new system if they can
be very sure that it reduced billing time by at least 5 days. At the 1% level of significance, does it
appear that the new billing system has lowered the billing time by at least 5 days?
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