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Lecture 15

STAT 101 Lecture Notes - Lecture 15: Hospital-Acquired Infection, Standard Deviation, Decision RulePremium


Department
Statistics
Course Code
STAT 101
Professor
Richard Waterman
Lecture
15

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Stat 101 - Introduction to Business Statistics - Lecture 15: Quality Control
To Understand Quality Control Chart, You must Master:
1. Central Limit Theorem
2. Standard Error of x-bar
a.
3. Surprise Paradigm
4. Type I (False positive) and Type II (False negative) errors
Quality Control
One popular use of statistics is in Quality Control (QC).
Examples:
Monitoring the proportion of defective silicon chips. Monitoring the average length
of time to resolve a call in a call center.
Monitoring the number of nosocomial infections each day in a hospital.
These are all sequences over time with inherent variability.
*****The key question is whether or not a jump in the observed process indicates that
something real has happened (a change in the process mean) or whether it is just noise
in the system.
Quality control procedures will allow us to formalize a process to help us make
this decision (signal change or noise).
Surprise Paradigm
On observing a rare event, doubt the assumptions under which that event was defined to
be rare -- Statisticians don’t believe in miracles
The Paradigm:
We have a belief.
Assuming this belief is true, we calculate the probability of an event of interest.
If we observe this event and the probability is small we have reason to reject this
belief.
In this way we learn.
● Examples..
○ Lottery
Belief: a lottery is fair – each ticket is equally likely to win.
Event of interest: a specific ticket wins.
Observed event: the President wins the lottery.
Learning: don’t play this lottery.
Higgs Boson
Belief: a Higgs type particle does not exist.
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Event of interest: certain decay products of collision in given proportions
are observed.
Observed event: decay products are seen in the right proportions, with a
very small probability (5-σ) under the non-existence hypothesis.
Learning: Overturn the initial belief of non-existence and conclude that the
data supports the existence of a Higgs type particle.
Newsfeed Data Example
A social networking site was worried that the introduction of a new browser version might
in some fashion degrade the user experience for a newsfeed type page. The user
experience was focused on the time to load the page completely.
The company randomly sampled 100 users each day from the US population of
all users with the browser in question, and who would be likely to update to the
latest version of the browser (though they might not all update at the same time).
Every day the company asked the respondents to rate their experience regarding
the loading of the time-line on a 1-10 scale with 10 being very positive.
The question is whether there is any evidence that the new browser is creating a
problem.
Historical experiments had suggested a mean rating of 8 with a standard
deviation of 1.2 would be reasonable proxies for µ and σ, the original process
mean and standard deviation.
Shape of distribution:
it is discrete, but mound shaped. The upper bound of the scale at 10 creates
some asymmetry (left-skewness) in the ratings.
But, from the Central Limit Theorem, we know that under certain conditions (iid
sampling) sample means from this distribution will be normally distributed.
The condition we will use is n > 10 |K4|, where n is the sample size and |
K4| is the kurtosis as defined in the module 13.
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