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This is a fairly easy homework assignment. I am just crowded with many other assignments to do right now. If you know statistics, it should be fairly easy. Requires minimal writing (answering questions), mainly problem-solving. If the writer is an expert at math, this should be fairly easy. It’s a Statistics 1 course.

# Exercise 1 – 80% Confidence Intervals

The idea of an 80% confidence interval is that the interval captures the true parameter value in 80% of all samples.  That’s not high enough confidence for practical use, but 80% hits and 20% misses make it easy to see how a confidence interval behaves in repeated samples from the same population.  Go to the Confidence Interval  applet.

• Set the confidence level to 80%. Click “sample” to choose an SRS and calculate the confidence interval.  Do this 10 times to simulate 10 SRSs with their 10 confidence intervals.  How many of the 10 intervals captured the true mean ?  How many missed?

• You see that we can’t predict whether the next sample will hit or miss. The confidence level, however, tells us what percent will hit in the long run.  Reset the applet and click “Sample 50” to get the confidence intervals from 50 SRSs.  How many hit?  Keep clicking “Sample 50” and record the percent of hits among 100, 200, 300, 400, 500, 600, 700, 800, and 1000 SRSs.  Even 1000 samples is not truly “the long run,” but we expect the percent of hits in 1000 samples to be fairly close to the confidence level, 80%.

## Percentage

50
100
200
300
400
500
600
700
800
1000

Exercise 2 – What confidence means.

Confidence tells us how often our method will produce an interval that captures the true population parameter if we use  the method a very large number of times.  The Confidence Interval applet allows us to actually use the method many times.

• Set the confidence level to 90%. Click “Sample 50” to choose 50 SRSs and calculate the confidence intervals.  How many captured the true population mean ?  Keep clicking “Sample 50” until you have 1000 samples.  What percent of the 1000 confidence intervals captured the true ?

• Now choose 95% confidence. Look carefully when you first click “Sample 50.”  Are these intervals longer or shorter than the 90% confidence intervals?  Again take 1000 samples.  What percent of the intervals capture the true ?

• Do the same thing for 99% confidence. What percent of 1000 samples gave confidence intervals that caught the true mean?  Did the behavior of many intervals for the three confidence levels closely reflect the choice of confidence level?

Exercise 3 – JAVA applet of critical values.

The last row of the table on the back cover of your text shows critical values for the standard Normal distribution.  Go to the following website: HyperStat Online: Statistical Analysis (http://davidmlane.com/hyperstat/z_table.html) to verify that the critical value needed for 95% confidence is z =1.96.  To do this, click on “Value from an area”, enter .95 in the “Area” box, and click on  “Between”.  The output should read -1.96 and 1.96, demonstrating that the critical value is z = 1.96.

No answer is required here.  You need to understand how the applet works before moving on to the next exercise.

### Exercise 4 – Confidence level 92.5%

What standard normal critical value z* is required for a 92.5% confidence interval for a population mean?  The value isn’t in the table on the back cover your text, but the website in Exercise 3 allows you to find it by specifying .925 in the area box.

Use your result to give the 92.5% confidence interval for the population mean in the following setting.  The yield (bushels per acre) of a variety of corn has standard deviation  bushels per acre.  Fifteen plots have these yields.

138.0

139.1

113.0

132.5

140.7

109.7

118.9

134.8

109.6

127.3

115.6

130.4

130.2

111.7

105.5