Introduction to Statistics Project #4

Part 1:

In this part of the project you will investigate sampling distributions and model for proportion of heads that may show up when a coin is tossed repeatedly. Toss the coins if you want, but it’s much easier to do a simulation with a calculator (or a computer –excel works well for this ). One way to do this is to generate 0’s and 1’s with equal probability, with 1 representing heads. By adding up all the 1’s you can effectively count the number of heads. Dividing that count by the number of tosses will result in \[\hat{p}\] , the sample proportion of heads.

On the TI 83 / 84 you can use the randInt command to randomly generate 0’s or 1’s:

1. select the "MATH" key,
2. arrow to the right to "PRB",
3. arrow key down to "5:randInt("
4. select "enter" ("randInt(" should be on the main screen)
5. enter "0,1)"
6. select "enter" (the output will randomly be either 0 or 1)

Selecting "enter" again and again will randomly output either 0 or 1. If you want the calculator to select ten random 0’s or 1’s in a row on step 5 above enter "0, 1, 10)". You will need to use the left and right arrow keys to view all of the 10 randomly selected 0’s and 1’s. By adding up all the 1’s you can effectively count the number of heads. Dividing that count by the number of tosses will result in \[\hat{p}\] , the sample proportion of heads.

1) Set up a calculator or computer’s random number generator to simulate flipping a coin 10 times.

2) Run 50 trials, recording all the sample proportions and make a relative frequency histogram of the results.

3) Repeat your simulation, this time tossing the coin 20 times. Again make a histogram of the 50 sample

proportions .

4) Compare the two distributions of the proportions of heads observed in your simulations from part 1 and 2.

5) Describe the theoretical sampling distribution model for 20 tosses.

6) Compare the mean and standard deviation of the actual distribution of your 50 sample proportions for 20

tosses to what the theoretical sampling distribution model says the mean and standard deviation should be.

7) Describe how your results might differ if you had run 50 tosses and 50 trials.

Part I

Educators have expressed concern that the economic impact of the events of September 11 may mean fewer students can afford to attend college. Some commentators have suggested that a heightened sense of patriotism may increase military enlistments, while others think that the existence of actual hostilities may deter young people from choosing a military path. A polling organization wants to investigate what this year’s high school seniors are planning to do after they graduate.

1. During the ‘90s about 63% of high school graduates enrolled in college. The pollsters hope to estimate the percentage of this year’s seniors planning to attend college with a margin of error no greater than 4%. What size sample would suffice if they want to have 90% confidence in the estimate?
   The pollsters randomly select 5 cities in Upstate New York and then randomly selected on high school in each city. The guidance office at each of the chosen schools is instructed to ask 100 randomly selected seniors what their current plans are, and to report the results back to the pollsters. The data collected from the 5 schools are summarized in the following table.

   Plans	Count
   College	289
   Employment	112
   Military	26
   Other (travel, parenting, etc.)	51
   Undecided / No response	22

2. Determine a 90% confidence interval for the percentage of seniors planning to go to college this year. Explain carefully what your interval means.
3. During the 90’s about 4.5% of high school seniors enlisted in the military. Do these data suggest that the percentage who enlist is different this year? Test an appropriate hypothesis and state your conclusion.
4. A few of the seniors did not respond to the guidance queries, and others said they were undecided. Some of the people might eventually decide to enlist in the military. Suppose that half of this small group also enlist. Would that cause you to change your conclusion in Question 3? Explain.

Price: $26.39

Solution: The downloadable solution consists of 14 pages, 1239 words and 26 charts.
Deliverable: Word Document