Assignment: Estimating a Parameter
Objective: In this project you will explore confidence intervals in a situation where the population parameter is actually known. You will see for yourself how repeat confidence intervals behave and you will see why we have to interpret them the way we do.Use Excel to crunch the numbers and provide the printout. I want to see all supporting work no matter what. You will lose credit without supporting work.
Part 1:
(a) Consider the procedure of flipping a fair coin a fixed number of times and observing X = the number of heads. Give three reasons why the random variable X qualifies as a Binomial random variable.
(b) If we define a success as "getting a head", then we already know what the expected true population proportion of heads is for a fair coin. p = _________ Remember, we usually do not know the value of this population parameter!!
Part 2:
(a) Even though we already know the true proportion of heads, p, we will use a sample and will create a confidence intervalestimate ofp. Suppose we want to create an 80% confidence interval and we are comfortable with a margin of error of 8%. Calculate the required sample size. Show your work.[STOP: Verify with your instructor to make sure you have the correct sample size before moving on. LET ME HELP YOU!]
n = __________
(b) Using the sample size determined in part (a), you will flip a coin n times and record X, the number of heads. The value of the point estimate is p ^= ________. Create an 80% confidence interval for p.Do not round until the end and keep three decimal places. Show your work.
(c) Did your confidence interval actually contain the true value of p? __________________
(d) If you plan to construct 20 different 80% confidence intervals for pbased on the same sample size, how many of them would you expect to contain the true value of p? Explain.
Part 3:
In this part of the project you will repeat the sampling procedure 20 times to create 20 different 80% confidence intervals for pbased on the same sample size you found in 2(a). Flipping a coin the required number of times is tedious. Luckily there is a website that will flip as many coins as you need all at once and will give you the total number of successes.
(a) Use the website to gather your sample data 20 different times. Record your results in the table on the next page, or make a pretty table in excel. You are business majors. Blow my mind with your l337 excel skillz.
(b) Construct each of the 20 different confidence intervals, one for each sample. Attach all calculations to this project. You will lose points if I don't get support work from you.
Go to the website:
Insert the desired sample size and click the button to get the results. Repeat 20 times.
Part 4: Complete this part AFTER you have generated all 20 of the confidence intervals.
(a) How many of the 20 different 80% confidence intervals actually contained the true value ofp? How did that compare to your answer from Part 2(d)?
(b) People who do not understand the theory behind confidence intervals will often interpret them incorrectly. Once an 80% confidence interval is constructed, some people will say, "There is a probability of 0.80 that the confidence interval contains the true value of p." Explain why this interpretation is VERY WRONG.
Part 3 Table:
Twenty different 80% Confidence Intervals for P. KEEP THREE DIGITS AFTER THE DECIMAL.
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Sample Results X = number of heads
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Point Estimate
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80% Confidence Interval forp
Write them in the form:
(LOW value, HIGH value)
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Does the Interval Contain the True Value of p?
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Attachment:- Website.rar