Part 3 Bayes Theorem A. A friend in need You and a friend decide for Sprin g Bre

Question

Part 3 Bayes Theorem A. A friend in need You and a friend decide for Sprin g Break to see Glacier Bay National Park https/www.nps.gov/glba/index.htm). You take the "inside passage" http:/lwww.alaska.org/cruises/inside-passage). Unfortunately, once on the boat, your friend becomes increasingly ill. At the next port of call, Juneau, Alaska. you decide to get off and get your friend to a hospital. Everybody says it's only seasickness, but once on land, things do not improve (What follows is fictitious). So after asking around you find two possible hospitals. Hospital A has a mortality rate of 0.1%, which means that of 1000 patients only 1 dies at the hospital on average. Hospital B has a mortality rate of 0.7% In other words, Hospital A has a better mortality rate than Hospital B Everyone in town, however, recommends Hospital B What's going on? Explain how the hospital with the higher mortality rate is best. B. Amazon deal You go to Amazon to buy a book; but the book, at the price you want, is only available through three resellers. Here are their ratings 94% positive out of 85 reviews 98% positive out of 20 reviews 99% positive out of 8 reviews · Which reseller is likely to give you the best service? Do you change your answer if the rating were as follows: 94% positive out of 850 reviews 98% positive out of 200 reviews · · Scanned by Cam 99% positive out of 80 reviews

Explanation / Answer

1)A friend in need

Given: Hospital A mortality rate = 0.1%

Hospital B mortality rate = 0.7%

Still people suggest hospital B

Possible reason:

Hospital B might have treated large number of patients and thus mortality rate is almost constant

On the other hand, hospital A might have treated people with small sample size.

Thus, even though the mortality rate seems low there can be drift in conditions and standard deviation making it unsuitable choice

2)Amazon deal

Its not always about accuracy but its also about sample size that has been used.

For a given standard deviation we divide it by square root of sample size to get actual standard deviation (deviation for large population)

The larger the sample size, the more precise the mean

In 1st case number of reviews is less(85,20,8) thus we can choose the one with highest accuracy

In 2nd case (850,200,80) sample size is large thus we will prefer the one with larger sample size

4)Fair coin

Again here tossing coin has fixed probability associated with it 0.5 for head/tail

But as we go for less number of samples the accuracy of prediction will be less. But as we go on repeating experiment we will reach the expected value of probability

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