In 2015, the average duration of long-distance telephone calls from a certain town was 3.9 minutes. A telephone company wants to perform a test to determine whether this average duration of long-distance calls has changed. Fifty calls, originating from the town, were randomly selected, and the following summary minutes. ∑ ? = 205 ∑(? − ?̅)2 = 56.43 Using the p-value approach at the 1% level of significance, test whether the mean duration of long-distance calls from the town had increased. Construct the 99% confidence interval for the population mean duration of the long-distance calls from the
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 2015, the average duration of long-distance telephone calls from a certain town was 3.9 minutes. A telephone company wants to perform a test to determine whether this average duration of long-distance calls has changed. Fifty calls, originating from the town, were randomly selected, and the following summary minutes.
∑ ? = 205 ∑(? − ?̅)2 = 56.43
- Using the p-value approach at the 1% level of significance, test whether the mean duration of long-distance calls from the town had increased.
- Construct the 99% confidence interval for the population mean duration of the long-distance calls from the
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