SOLUTION: I am in serious need of help. How do i build a 95% confidence interval with only just orange M&M's? Number of M&Ms ----------- ----------- --- ORANGE TOTAL 6

Algebra ->  Statistics  -> Confidence-intervals -> SOLUTION: I am in serious need of help. How do i build a 95% confidence interval with only just orange M&M's? Number of M&Ms ----------- ----------- --- ORANGE TOTAL 6       Log On


   

Question 1127983: I am in serious need of help. How do i build a 95% confidence interval with only just orange M&M's? Number of M&Ms
---------------------------
ORANGE TOTAL
6 20
5 17
3 17
1 17
5 19
6 18
2 20
4 19
6 18
3 20
6 17
3 16
4 18
3 17
5 17
5 18
4 19
3 19
4 20
2 17
4 18
7 19
4 18
6 19
5 18
---------------------------
106 455
======== ========
p-hat = 0.23
n = 455


Construct the 95% confidence interval around the true population porportion of orange colored M&Ms in a fun-sized bag of plain M&Ms.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

For the standard normal distribution there is a 95% probability that a standard normal variable, Z, will fall between -1.96 and 1.96.
In other words,
P%28-1.96+%3CZ%3C+1.96%29=0.95
p-hat+=0.23
n+=455
p-hat%2B-Z%2Asqrt%28p-hat%281-p-hat%29%2Fn%29
0.23%2B-1.96%2Asqrt%28%280.23%281-0.23%29%29%2F455%29
0.23%2B-1.96%2Asqrt%28%280.23%2A0.77%29%2F455%29
0.23%2B-1.96%2Asqrt%280.1771%2F455%29
0.23%2B-1.96%2Asqrt%280.00038923076923%29
0.23%2B-1.96%2A0.019728932288
0.23%2B-0.03866870728448
so,
0.23%2B0.03866870728448=+0.2686679968
0.23-0.03866870728448=+0.1913320032

Confidence Interval is: (0.1913320032,+0.2686679968)