hw.backwardsZ.CI

hw.backwardsZ.CI - 9/21/2010 HW.backwardsZ.CI.&KEY

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Unformatted text preview: 9/21/2010 HW.backwardsZ.CI.&KEY hw.backwardsZ.CI.&KEY.doc Page 1 Backwards Z, CI Revised 09/20/10 FOR ALL HOMEWORK. [1] IF MORE THAN ONE PAGE, THEY MUST BE STAPLED. OTHERWISE, NO CREDIT. [2] NO RIPPED-OUT EDGES OF PAPER – ALL EDGES MUST BE SMOOTH FOR CREDIT. [3] SHOW ALL WORK, INCLUDING FORMULAS WITHOUT NUMBERS, USING SYMBOLS. [4] TURN IN **BEFORE YOU SIT DOWN** EVEN IF I’M LECTURING. OTHERWISE NO CREDIT. [5] UPPER RIGHT CORNER MUST HAVE YOUR CLASS ID _ Suppose all the X (using samples of size 25) from a population distribution could be collected into their own distribution, where they would be normally distributed with a mean of 20 and a variance of 16/25 _ ⎛ σ2 ⎞ which means X ∼N⎜μ, n ⎟ . (It is therefore also true that X ∼N(μ,σ2) which is the population ⎝ ⎠ distribution.) _ #1. Looking at all possible Xs in this sampling distribution, about 96.99% of them will exceed some number _ y. Another way to state this is: P(X > y) = 0.9699. Show work (including formulas without numbers) in computing the value of y. Draw the normal graph with both axes and label everything and show with an arrow the area you are looking for, as you’ll need to do for an exam. _ #2. Same population distribution and sampling distribution. Looking at all possible Xs in this sampling _ distribution, about 40.9% of them will be less than some number y. Another way to state this is: P(X < y) = 0.409. Show work (including formulas without numbers) in computing the value of y. Draw the normal graph with both axes and label everything and show with an arrow the area you are looking for, as you’ll need to do for an exam. NEW PROBLEM (Unrelated to the previous problems.) #3. CI for the mean: The population of X's is normally distributed. A sample of 9 was taken, which gave a mean of 4 and a standard deviation of 5. a. This is a CI for what? Symbol: _______ b. What is the symbol related to the number 9?____ c. What is the symbol for the 4?______ d. What is the symbol for the 5?______ e. Show work including first the symbols without numbers in constructing a 90% CI for the mean. f. Give the interpretation as specified in class for this CI. NEW PROBLEM (Unrelated to the previous problems.) #4. The population of Xs is normally distributed. A sample of 100 was taken, which gave a mean of 25 and standard deviation of 16. We happen to know that the population standard deviation is 12, although we don’t know the population mean. a. This is a CI for what? Symbol: _______ b. What is the symbol related to the number 100?____ c. What is the symbol for the 25?______ d. What is the symbol for the 16?______ e. What is the symbol for the 12?______ f. Show work including first the symbols without numbers in constructing a 95% CI for the mean. end g. Give the interpretation as specified in class for this CI. ...
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This note was uploaded on 01/31/2012 for the course PROB 343 taught by Professor Hin during the Spring '11 term at Adrian College.

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