95% confidence interval

one hundred people agreed to drink from unmarked cans and indicated which drink they liked better; 54 said company A. Construct and interpret the corresponding 95% confident interval for p, the rue proportion of people who prefer Company A to B.


54 - 1.96(standard dev/10), 54 + 1.96(standard dev/10)

but how do I find the standard deviation?

thanks

WlND said:

one hundred people agreed to drink from unmarked cans and indicated which drink they liked better; 54 said company A. Construct and interpret the corresponding 95% confident interval for p, the rue proportion of people who prefer Company A to B.


54 - 1.96(standard dev/10), 54 + 1.96(standard dev/10)

but how do I find the standard deviation?

thanks

Click to expand...

You can find the standard deviation if you have a Binomial Distribution. What are the three criteria?
a) Is it a yes/no question? Yes, answers are either A or B.
b) Is there a fixed number of trials? Yes, n=100.
c) Is the probability of success constant for all trials? Yes, there is a "true" proportion p (which is unknown).
Since all three criteria are met, use the properties of the Binomial Distribution to find the standard deviation.