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Confidence Interval

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Problem: From the Data Set below select a sample of 20 values and find the 90% confidence interval of the mean of the number of the acres. Find the mean of all values, and determine if the confidence interval contains the mean.

DATA SET VI
Acreage of U.S. National Parks, in Thousands of Acres
41 66 233 775 169
36 338 223 46 64
183 4724 61 1449 7075
1013 3225 1181 308 77
520 77 27 217 5
539 3575 650 462 1670
2574 106 52 52 236
505 913 94 75 265
402 196 70 13 132
28 7656 2220 760 143

https://brainmass.com/statistics/confidence-interval/256900

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From the Data Set below select a sample of 20 values and find the 90% confidence interval of the mean of the number of the acres. Find the mean of all values, and determine if the confidence interval contains the mean.

DATA SET VI
Acreage of U.S. National Parks, in Thousands of Acres
41     66   233    775     169
36    338   223     46      64
183   4724    61   1449    7075
1013  3225   1181    308      77
520    77     27    217       5
539  3575    650    462    1670
2574   106     52     52     236
505   913     94     75     265
402   196     70     13     132
28  7656   2220    760     143

Step 1: We select a sample of 20 ...

Solution Summary

From the given Data Set the solution selects a sample of 20 values and finds the 90% confidence interval of the mean of the number of the acres, find the mean of all values, and determines if the confidence interval contains the mean.

\$2.19

Confidence Intervals, Samples, and Unknown Variance

Let (X1, X2,..., Xn) be a sample, where each Xi is a random variable of normal distribution with mean mu and variance sigma². Let us suppose that n = 20, and sigma² = 9. An experiment has yielded the results (X1, X2,..., X20), and we have calculated that the empirical mean x20 = 2.09.

1) Give a confidence interval with level of confidence 90% for mu.

2) How big would the sample have to be for the interval to be half as long?

3) Let us now suppose the variance is not known. Knowing that counting from i=1 to 20 (xi - x20)² = 14.6, give a confidence interval with level of confidence 90% for the value of mu.

4) We now suppose we know mu is known and is equal to 2. Give a confidence interval with a confidence level of 90% for the value of sigma².

5) Same question if we do not know the value of mu.

Please see attachment for proper format.

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