Suppose that we survey 30 employees of a big company and ask each whether they support the new policy on retirement funding. Only 6 employees support the policy. By using most likelihood approach, estimate the probability p, the true but unknown proportion of employees that support the policy.
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6/30 = 1/5
i want to know how we use the most likelihood approach to know the unknown proportion of employees that support the policy
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Please may i know the Most Likelihood approach? thats what i am stuck at.
In statistics, maximum-likelihood estimation (MLE) is a method of estimating the parameters of a statistical model. When applied to a data set and given a statistical model, maximum-likelihood estimation provides estimates for the model's parameters. - Wikipedia
how does that apply to the problem is what i want to know...
Okay, here is what I have learned:
The MLE approach is used when you don't have the time or resources to take a measurement (whatever that may be) from an entire group, or if this task is simply impossible. So say you wanted to know the mean length of all the alligators in the Florida Everglades. Obviously it would be too hard to go through, catch, and measure all of them. Now assuming that the gators are normally distributed, in other words, you don't have a huge population of large or small gators in one region, you can take a small sample of gators and measure them. Then you can apply MLE to get an estimate of the mean length of all the gators in the Everglades.
So, in your problem you have a small sample (30) of a large company. Using MLE you can fairly accurately estimate the numer of supporters of the policy assuming that the company as a whole has a normal distribution of supporter. Variance also comes into play here, but that's where I get confused.