Generate a random sample of 10 00 numbers from a normal distribution, selecting the parameters so that 99.7% of the numbers are expected to fall in the interval (0,18 ). Use your own random seed. Do not show the sample.

1a) Your 1st chart: Show the summary statistics for this sample.( Tools/Data Analysis)

b) Your 2nd chart: Select bins 0, 1,...,19 and make a well-labeled and proportioned histogram for this data set.

c) Compute the relative error in using \(\bar{x}\text{ and s as point estimates of }\mu \text{ and }\sigma \text{.}\) You do this, for example, as \(error=\frac{\left| \bar{x}-\mu \right|}{\mu }(100)%\). Show the Excel formulas ( your parameters are different):

Now generate a random sample of 10 00 numbers from the uniform distribution on [0,18 ]. Use the random seed as above. Do not show the sample .

2a) Your 1st chart is as above. b) Your 2nd chart is as above, but use bins 0 to18 c) Do the same 2 calculations of relative error as above.

Central Limit Theorem Experiment.

Generate 500 samples of size 36 from the uniform population above. Use the function =rand()*18 . Each row will be a sample. You will have 500 rows of 36 uniform numbers. Save these samples so that they do not change as you continue. Compute the sample mean for each row using =average(__:__). Now you will have a column of 500 sample means.

3a) Your 1st chart: Show the summary statistics for these sample means.

b) Your 2nd chart: Using bins starting with 6.5 and increasing 0.5 increments to 11.5,make an appropriately labeled and proportioned histogram for the means.

c) The underlying variable is uniform. In a complete sentence: What evidence of distribution type do you see in the histogram of the uniform sample means?

Type and fill in the blank:

d) For the uniform distribution on [0,18], the population standard deviation is _________.

e) For samples of size 35 for this population, the theoretical value of \({{\sigma }_{{\bar{x}}}}\) is ___________.

f) The observed value of \({{s}_{{\bar{x}}}}\) is ________.

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Solution: The downloadable solution consists of 6 pages, 520 words and 4 charts.
Deliverable: Word Document