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a)Again, select "Analyze" and the details about each interval will be loaded into the spreadsheet on StatCrunch.Use StatCrunch to make ahistogram(with an overlaid Normal curve) and aQQ plot(with the correlation value) for the new column labeled "Sample Proportion."Paste both plots below.

b)Comparethe plots you just found to those found in #1.Which distribution is closer to Normal?Whydoes this make sense?

This chart is closer to normal. This makes sense because n=75.

Part 2: Means

Data File-WA5.Africa.GDP(on Blackboard)

The data (as reported by IMF databases) is the GDP per capita* in 2017 for African countries.This lab will demonstrate what a confidence interval is intended to do (capture the true parameter value, in this case the mean).Realistically, we will not know what that true value is and that is the reason for finding a confidence interval.

*Nominal GDP per capita-a measure of the country's income in USD($) with respect to the country's population, discounting inflation

1.a)The first two columns show the names of the 54 recognized African countries (the population) and their 2017 GDPs per capita.Begin by using StatCrunch to look at thehistogramandQQ plotfor theGDPs to see what the overall distribution looks like.Pastethe plots below.

b)Based on the plots, whatshapedoes the distribution of African GDPs have andwhy?

Histogram shows Right skewed. Maybe because the GDP's start of at a high numerical value and then decrease over time. QQ plot shows left skewed. Maybe for the vice versa reason of the histogram.

c)What are the values of themean(this is), thestandard deviation(this is) and themedian?

Keep this in mind when looking at your results in the remaining questions.

2.a)Use StatCrunch to select3 SRSsofsize 32(use the DataSample feature introduced in the last lab).Include asnapshotof your results here.

b)Find the mean for each sample.

Sample 1=

Sample 2=

Sample 3=

c)Is it safe to apply theCentral Limit Theoremto the sampling distribution of all such means (from samples like those in the last problem)? Could we usesmallersamples?

Use the Sampling distributions Applet introduced in the last lab (select DataSampling Distributions).Choose to samplefrom the GDP data(select"From data table") and look at themean.Trysample sizesof10,20, and32, choosing1000 samples(choose "1000 times") each time.What do you notice?Particularly,discuss the change in theshapeof the sampling distributionand standard deviationof themeans.

(This should support thatseem to be anappropriatesample size.)

3.Now you are going to calculate three95% confidenceintervals for the populationmeanbased on the three samples that you selected.

a)Use the Normal calculator in StatCrunch to find thecritical values(Z*). Also, include thegraphfrom StatCrunch that shows both critical values.

b)Find thesampling errorthat you will use for each interval. (This valuewill be the samefor each interval.)

(Recall the sample size,n, is32.)

c)What is the value of themargin of (sampling) error?

d)Use yoursample means(from 4b) and themargin of errorto findthree 95% confidence intervalsfor thepopulation mean.

Report thelowerandupper limitsof each confidence interval below by using our general formula:.

oInterval 1

oInterval 2

oInterval 3

4.You can calculate the intervals with StatCrunch by selectingSTATZ StatisticsOne Samplewith data.

Select thesamples(column names that correspond to your samples) andenterthestandard deviation().

Select"Confidence Interval"and then from the list of"Optional Graphs and Tables"select"Confidence interval plot."Click"Compute!".

First you should see results that match what you found in #5: Sample Mean, the Standard Error (Sampling Error), and the Lower and Upper Limits for the Confidence Interval.Check to make sure that the mean and sampling error match your previous findings.

Click the right arrow to see the confidence interval plots andpaste all three plotsbelow.

5.Mark down thepopulation mean valuethat you previously found in #3.How manyof your confidence intervalscontainthis value? (It will likely be all three.)Does your answermake sensewhen considering the confidence level?Why?

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