Question 1 In 2002, the average duration of incoming telephone calls to a furniture store was 9.4 minutes. The manager wants to perform a test to determine whether this average duration of incoming calls has changed. Twenty calls to the store was randomly selected and the mean duration was 10.2 minutes with standard deviation 4.8 minutes. Using a 1% level of significance, test whether the mean duration of incoming calls to the store had changed. Construct the 95% confidence interval for the population mean duration of the incoming calls to the furniture store.
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!
Question 1
In 2002, the average duration of incoming telephone calls to a furniture store was 9.4 minutes. The manager wants to perform a test to determine whether this average duration of incoming calls has changed. Twenty calls to the store was randomly selected and the mean duration was 10.2 minutes with standard deviation 4.8 minutes.
- Using a 1% level of significance, test whether the mean duration of incoming calls to the store had changed.
- Construct the 95% confidence interval for the population mean duration of the incoming calls to the furniture store.
Question 2
A recent survey showed that from a sample of 500 packages delivered by a Postal Service, 480 were delivered on time.
- Construct a 95% confidence interval for the proportion of all packages that are delivered on time by the Postal Service.
- The manager of the Postal Services claims that 98 percent of their mail are delivered on time. Test at the 1% significance level to determine whether the true proportion is less than 98 percent.
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