probability & Stats - Estimating Parameters

Statistics
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Mar 3rd, 2015

1) Presumably you would have to obtain an estimate of this yourself, perhaps by surveying the students (i.e. taking a sample, and using that to estimate the proportion of all students that are parents). 

You would have to carefully consider how to obtain this sample though, in order for it to be balanced (be a non-biased reflection of the whole student body). So, you might survey students at random from each class, across different times of day, making sure to have a mix of ages, gender, majors etc. in your sample that is close to the overall mix for the student body.

2) No, you would not, since this is very likely to be a biased sample. Since you have only one campus, and one time represented in your sample, if these are correlated with the statistic you are interested in (parenthood) your estimate of 25% and the true overall number might be very different. For example, perhaps parents are less likely to sleep in and miss 9:30am classes, if they have to send their children to school, and so 25% may be an overestimate.

3) The trade-off is between precision and certainty. For any estimate, you can increase its precision (0-100% range down to a more useful 20-30% range) but at the cost of certainty (you can be decreasingly confident that the true value lies in your estimated range). Often we use 'standard' precision/certainty trade-offs (e.g. 90% and 95% confidence intervals are commonly used) but in real life situations this trade-off will depend on what your aim is: For example you may need to be much more certain about the likelihood of negative side-effects from a new drug, or about evidence that is used to convict somebody of a crime.


Hope this helped!

Mar 3rd, 2015

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