question archive I have a question for my political science statistics course! I'm currently learning about standard deviation and standard error, and we're doing a project with M&M's to demonstrate these ideas
I have a question for my political science statistics course! I'm currently learning about standard deviation and standard error, and we're doing a project with M&M's to demonstrate these ideas
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I have a question for my political science statistics course! I'm currently learning about standard deviation and standard error, and we're doing a project with M&M's to demonstrate these ideas. I'm having a lot of trouble figuring out what values I should use to calculate the standard deviation, and it's keeping me from completing the rest of the project.
I've attached the questions from the assignment, as well as the answers I've already found.
1) What is the total number of orange M&Ms in this bag?
- 30 total orange M&Ms
2) What is the total number of M&Ms in this bag of any color (including orange)?
- 103 total M&Ms
3) What proportion of your bag is orange?
To calculate this quantity, divide the number of orange by the number of any color.
- 30 / 103 = 0.291
4) What is the standard deviation of this variable?
- What values should I be using for this calculation? So lost...
5) What is the standard error of the proportion orange in this bag?
- Same problems as question 4
6) What is the 95% confidence interval of the proportion orange in this bag? Enter the lower and upper bounds of this interval.
Lower bound: jQuery224029122629061890226_1614294028658
Upper bound: ??
Please let me know if you need any other information to help me with the project. I would appreciate it if you could list the steps, as I need to repeat the project with a second bag.
Thank you in advance!
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4.) Standard deviation = 0.4542
5.) Standard error = 0.0448
6.) Lower bound = 0.203
Upper bound= 0.379
Step-by-step explanation
From the information given above,
x = 30 - the total number of orange M&Ms in this bag
n = 103 - the total number of M&Ms in this bag of any color
The proportion that the bag is orange is given as;
p=nx?=10330? = 0.291
4. ) The standard deviation of this variable is calculated using the following formula;
Standard deviation =p(1−p)?
=0.291(1−0.291)?
= 0.291(0.709)?
= 0.206319?
= 0.4542
5.) The standard error of the proportion orange in this bag is calculated using the following formula;
Standard error = np(1−p)??
= nstandard deviation2??
= 1030.45422??
= 0.002003?
= 0.0448
6.) The 95% confidence interval of the proportion orange in this bag is calculated as follows;
p±Zα/2?∗np(1−p)?? = p±Zα/2?∗standard error
Where;
p = 0.291
standard error = 0.0448 -
Zα/2?=Z0.05/2?=Z0.025?=Z0.975? = 1.96 - obtained from z statistical tables.
Lower bound = 0.291−1.96∗0.0448
= 0.291 - 0.088
= 0.203
Upper bound = 0.291+1.96∗0.0448
= 0.291 - 0.088
= 0.379
