Description

math homework, need use excel or any stats software. Please check the file that I uploaded, thanks

2 attachmentsSlide 1 of 2attachment_1attachment_1attachment_2attachment_2

Unformatted Attachment Preview

Math 324 Probability and Statistics with Computing

Project 3 Confidence Intervals

Objective: Explore a confidence interval estimation through simulation and random sampling.

You may use MS Excel, Google Sheets, or any other statistical software of your choice. If you

use R or Python, you will submit the source code and the output.

Introduction: Here’s the game: there are two boxes with four balls each. To play, you put on a

blindfold and then pick one ball at random from each box.

There are two red, one blue and one green ball in the box on the left. There are two blue, one red

and one green ball in the box on the right.

Payouts:

•

•

•

•

$0 if the balls are different colors,

$0.50 if they are both red,

$1 if they are both blue, and

$16 if they are both green.

It costs $1 to play the game.

Let 𝑋𝑋 be the overall amount of money you end up with (won or lost) after playing the game. This

includes the cost of the game. For instance, if on a given game you win $16 but paid $1 to play the

game, you walk away with $15. Thus, in this case 𝑋𝑋 = $15. On the other hand, if you did not win

($0) but paid $1 to play, then 𝑋𝑋 = −$1.

Project Instructions:

1. State the probability distribution of the variable 𝑋𝑋.

2. Find the mean (𝜇𝜇) and the standard deviation (𝜎𝜎) of 𝑋𝑋.

3. Randomly sample data from this distribution. Generate 1000 samples of size 𝑛𝑛 = 50.

4. Summarize the data generated (50000 values) into a relative frequency table to confirm the

data follow the theoretical distribution in step 1.

5. Compute a sample mean from the data in each sample. There should be 1000 sample

means.

6. Make a histogram of the sample means. You may use the bins of your choice. (According

to the CLT, the distribution of the 𝑋𝑋� variable is approximately normal. Does the graph look

bell-shaped?)

7. Choose a 95% confidence level and use 𝜎𝜎 from step 2 to compute the associated margin of

error.

8. For each sample, compute a 95% 𝑧𝑧-confidence interval. There should be 1000 confidence

intervals.

9. What percentage of these confidence intervals contain the true population mean you found

in step 2?

Some MS Excel function you may need to complete this project:

RAND, VLOOKUP, SUMPRODUCT, COUNTIF, COUNTIFS, AVERAGE,

NORM.S.INV, CONFIDENCE.NORM

Be sure to organize your work in such a way that it looks presentable and is easy to follow!

Math 324 Probability and Statistics with Computing

Project 3 Confidence Intervals

Objective: Explore a confidence interval estimation through simulation and random sampling.

You may use MS Excel, Google Sheets, or any other statistical software of your choice. If you

use R or Python, you will submit the source code and the output.

Introduction: Here’s the game: there are two boxes with four balls each. To play, you put on a

blindfold and then pick one ball at random from each box.

There are two red, one blue and one green ball in the box on the left. There are two blue, one red

and one green ball in the box on the right.

Payouts:

•

•

•

•

$0 if the balls are different colors,

$0.50 if they are both red,

$1 if they are both blue, and

$16 if they are both green.

It costs $1 to play the game.

Let 𝑋𝑋 be the overall amount of money you end up with (won or lost) after playing the game. This

includes the cost of the game. For instance, if on a given game you win $16 but paid $1 to play the

game, you walk away with $15. Thus, in this case 𝑋𝑋 = $15. On the other hand, if you did not win

($0) but paid $1 to play, then 𝑋𝑋 = −$1.

Project Instructions:

1. State the probability distribution of the variable 𝑋𝑋.

2. Find the mean (𝜇𝜇) and the standard deviation (𝜎𝜎) of 𝑋𝑋.

3. Randomly sample data from this distribution. Generate 1000 samples of size 𝑛𝑛 = 50.

4. Summarize the data generated (50000 values) into a relative frequency table to confirm the

data follow the theoretical distribution in step 1.

5. Compute a sample mean from the data in each sample. There should be 1000 sample

means.

6. Make a histogram of the sample means. You may use the bins of your choice. (According

to the CLT, the distribution of the 𝑋𝑋� variable is approximately normal. Does the graph look

bell-shaped?)

7. Choose a 95% confidence level and use 𝜎𝜎 from step 2 to compute the associated margin of

error.

8. For each sample, compute a 95% 𝑧𝑧-confidence interval. There should be 1000 confidence

intervals.

9. What percentage of these confidence intervals contain the true population mean you found

in step 2?

Some MS Excel function you may need to complete this project:

RAND, VLOOKUP, SUMPRODUCT, COUNTIF, COUNTIFS, AVERAGE,

NORM.S.INV, CONFIDENCE.NORM

Be sure to organize your work in such a way that it looks presentable and is easy to follow!

Purchase answer to see full

attachment

Tags:

standard deviation

Math Problems

cumulative probability

stats software

User generated content is uploaded by users for the purposes of learning and should be used following Studypool’s honor code & terms of service.

## Reviews, comments, and love from our customers and community:

This page is having a slideshow that uses Javascript. Your browser either doesn't support Javascript or you have it turned off. To see this page as it is meant to appear please use a Javascript enabled browser.