A small local insurance company is looking to see if they have reached their 2020 goal of more than $30.20 in savings per family. In order to see if they met their goal, they randomly surveyed 50 of their over 1000 customers and found that they had saved an average of $32.12 with a standard deviation of $4.83. Is this strong evidence that they have attained their savings goal? a) Check the appropriate conditions to perform this test. State each condition and state whether it has been satisfied or not. b) Regardless of your answers to part (a), test an appropriate hypothesis and state your conclusion. Use a significance level of 0.05. (Use your calculator to conduct this test. Do not do the calculations by hand.)
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!
A small local insurance company is looking to see if they have reached their 2020 goal of
more than $30.20 in savings per family. In order to see if they met their goal, they randomly
surveyed 50 of their over 1000 customers and found that they had saved an average of
$32.12 with a standard deviation of $4.83. Is this strong evidence that they have attained
their savings goal?
a) Check the appropriate conditions to perform this test. State each condition and state
whether it has been satisfied or not.
b) Regardless of your answers to part (a), test an appropriate hypothesis and state your
conclusion. Use a significance level of 0.05. (Use your calculator to conduct this test. Do
not do the calculations by hand.)
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