The document discusses the application of confidence intervals and normal distribution in conservation biology, particularly focusing on bear populations. It defines key concepts like confidence intervals, population mean, variance, point estimates, and critical values, illustrating their significance with examples related to bear data. The importance of these statistical tools in estimating population characteristics and improving understanding of bear demographics is emphasized.

1. Confidence Intervals in the Life Sciences Presentation
Names
Statistics for the Life Sciences STAT/167
Date
Fahad M. Gohar M.S.A.S
1
Conservation Biology of Bears
Normal Distribution
Standard normal distribution
Confidence Interval
Population Mean
Population Variance
Confidence Level
Point Estimate
Critical Value
Margin of Error
Welcome to the presentation on Confidence Intervals of
Conservation Biology on Bears.
The team will define normal distribution and use an example of
variables why this is important. A standard and normal
distribution is discussed as well as the difference between
standard and other normal distributions. Confidence interval
will be defined and how it is used in Conservation Biology and
Bears. We will learn how a confidence interval helps
researchers estimate of population mean and population

2. variance. The presenters defined a point estimate and try to
explain how a point estimate found from a confidence interval.
Confidence level is defined and a short explanation of
confidence level is related to the confidence interval. Lastly, a
critical value and margin of error are explained with examples
from the Statdisk.
2
Normal Distribution
A normal distribution is one which has the mean, median, and
mode are the same and the standard deviations are apart from
the mean in the probabilities that go with the empirical rule.
Not all data has the measures of central tendency, since some
data sets may not have one unique value which occurs more
than once. But every data set has a mean and median. The mean
is only good with interval and ratio data, while the median can
be used with interval, ratio and ordinal data. Mean is used when
they're a lot of outliers, and median is used when there are few.
The normal distribution is continuous, and has only two
parameters - mean and variance. The mean can be any positive
number and variance can be any positive number (can't be
negative - the mean and variance), so there are an infinite
number of normal distributions. You want your data to represent
the population distribution because when you make claims from
the distribution of the sample you took, you want it to represent
the whole entire population.
Some examples in the business world: Some industries which
use normal distributions are pharmaceutical companies. They
model the average blood pressure through normal distributions,
and can make medicine which will help majority of the people
with high blood pressure. A company can also model its average
time to create something using the normal distribution. Several

3. statistics can be calculated with the normal distribution, and
hypothesis tests can be done with the normal distribution which
models the average time.
Our chosen life science is BEARS. The age of the bears can be
modeled by normal distributions and it is important to monitor
since that tells us the average age of the bear, and can tell us a
lot about the population. If the mean is high and the standard
deviation is low, this means there are very low young ones, and
this is a problem. If the mean is low and the standard deviation
is low, this means the mothers and fathers of the children are
either gone or have been poached. Such measures tell us a lot
about the population. Using the normal distribution, we can see
what percentage of the bear population is above a certain age.
The normal distribution can also model the head width, neck,
length, chest, weight etc. If the weight is modeled, a scientist
can find out what percentage of the bears have a certain weight,
and it helps the life scientists understand if the weights of the
bears are too low, thus food is scarce.
The distribution of the ages is approximately normal and
bimodal (mean is approx. equal to median). Given the mean and
standard deviation are 43.51825 and 33.72068 respectively, the
z-scores can be calculated and probabilities can be figured out.
3
Standard Normal Distribution
The standard normal distribution is a bell shaped representation
of data that is symmetrical and shows a correspondence between
area and probability. Normal distribution can have varying
levels of standard deviations as long as the mean stays the
same, but standard normal distribution always has a mean of 0,

4. a standard deviation of, and the total area under its density
curve equals 1.(M Triola, F. Triola)
By subtracting the mean from the chosen variable x and divide
by the standard deviation, you get the standard normal
distribution of z. (lbowen11235, 2010)
Applying this to the age of bears in our population, I’ll take the
total sample group of 54 bears and subtract the mean of
43.51852 and then divide by the standard deviation of 33.72068,
which then gives us a z score of 0.3108324, a mean of zero, and
a standard deviation of 1.
lbowen11235. (2010, October 22). Theory of Normal
Probability Calculations Using the Standard Normal Table
[Video file]. Retrieved from YouTube website:
http://www.youtube.com/watch?v=zCormwRIP9s
4
Confidence Interval
A confidence interval (or interval estimate) is a range (or an
interval) of values used to estimate the true value of a
population parameter.
A confidence interval is sometimes abbreviated as CI.
5
Confidence Interval (Population Mean)
The confidence interval can tell us what values the population

5. mean is within if the population mean is unknown. In this
example I found that the mean population age was between
36.82734 and 50.20916 with a margin of error E=6.690908 and
a confidence interval of 95%.
Each set of data, whether recording the bears neck, head width
or weight will each come up with a different population mean in
regards to the variable and the confidence interval.
6
Confidence Interval (Population Variance)
Population Variance: Square of the population standard
deviation (σ2).
Formulas on Calculating Variances
Calculate a 95% C.I. on variance for a sample (n = 35) with an
S of 2.3
The units of the standard deviation are the same as the units of
the original data, it is easier to understand the standard
deviation than
the variance. However, that same property makes it difficult to
compare variation for values taken from different populations.
The confidence intervals have many jobs. Earlier the presenters
discussed the standard normal distribution; this section is going
to discuss how a confidence interval is an interval, calculated
from the sample data that is very likely to cover the unknown
mean, variance, or proportion.
For example, after a process improvement a sampling has shown
that its yield has improved from 78% to 83%. But, what is the
interval in which the population’s yield lies? If the lower end of
the interval is 78% or less, you cannot say with any statistical
certainty that there has been a significant improvement to the
process. There is an error of estimation, or margin of error, or

6. standard error, between the sample statistic and the population
value of that statistic. The confidence interval defines that
margin of error or standard error, between the sample statistic
and the population value of that statistic. The confidence
interval defines that margin of error (Admin, 2006).
Admin. (2006) Six Sigma Tutorial, Confidence Interval.
Retrieved October 3, 2011 from http://sixsigmatutorial.com/six-
sigma-confidence-intervals-tutorial/411/
7
Confidence Level
Confidence level is the probability that the interval estimate
contains the population parameter.
Find the interval estimate
Assume n ≥ 30
located the confidence level “c” between the critical value -zc
and zc
Choose 95% confidence level with α= 0.05 for more precision.
The choice of 95% with = 0.05 is most common because it
provides a good balance between precision. (M.Triola & F
Triola) Therefore, our confidence level will lie between –Zc =
(α) and Zc = (α)
8
Point Estimate
Point estimate
The method for finding a point estimate (a single value)
A point estimator is the sample statistic

7. Point estimate: A point estimate of a population parameter is a
single value of a statistic. For example, the sample mean x is a
point estimate of the population mean μ. Similarly, the sample
proportion p is a point estimate of the population proportion P.
A point estimate is a single number that represents our best
guess for the value of the parameter whose value we are trying
to estimate.
The method for finding a point estimate (a single value) for a
population parameter involves the following steps:
Draw a random sample from the population.
Choose an appropriate sample statistic and compute its value
from the observed sample data.
Compute the value of the sample statistic and use it as an
estimate for the true population parameter in question.
A point estimator is the sample statistic (^) whose value is used
to estimate the true value of a population parameter.
p
(For example ^, is used to estimate p).
p
Psomas, N. (2003).Chapter 6 Point Estimation. Retrieved
October 1, 2011, from
http://www.marin.edu/~npsomas/Lectures/ch6_confidence_inter
vals.htm
9
Point Estimate and Datasets
Using the data set of bears we can calculate the estimate on the
sample size with 95% confidence level 1% margin of error. The
data set is useful for calculating the sample size to estimate

8. proportion (-1). The information will tell us the confidence
level and margin of Error, E. Finally, the data set calculates
what is needed for estimating the mean of a sample size.
In the data set above it tells us the age in months, gender of the
bears, head length, neck, and length of their body, chest size,
and weight. This data set is allowing a point estimate of
different information we are looking for. The data is also using
confident intervals for statistics. In the article, Population
Growth of Yellowstone Grizzly Bears, the researchers are using
the same information but different data to track their bear
research. This is telling us point estimates, error of margin, and
confidence levels are important in order to find any all
information the researchers are in need of (Harris, White,
Schwartz & Hardoldson, 2007).
Harris, R. B., White, G. C., Schwartz, C. C., & Haroldson, M.
A. (2007). Population growth of Yellowstone grizzly bears:
uncertainty and future monitoring. Ursus, 18(2), 168-178.
Retrieved from EBSCOhost.
10
Critical Value
The critical value is the value for which a certain percentage at
a tail is true. For example, for a z distribution, common critical
values are 2.576 (0.005 probability right/left tail), 1.96 (0.025
probability right/left tail), 1.645 (0.05 probability right/left
tail). Such values can also be computed for student’s t
distributions, f distributions, chi-square distributions, etc. These
values can be used to evaluate the confidence interval (times the
standard error). The formula is:
����±����_����� ((���.���.)/(������ ����))
In the given variable, the mean and standard deviation are
43.51825 and 33.72068 respectively. The z confidence interval
would be used here since the sample size is greater than 30, and

9. the confidence interval at 95% is:
11
Margin of Error
The margin of error E is the greatest possible distance between
the point estimate and the value of the parameter it is
estimating.
Confident interval for population proportion p
p’ – E < p < E + p’
Application to Conservation biology and BEARS
- Given n= 100; confidence level = 95% = 0.95; x = 10
- Margin error E =0.0587989
Confident interval 0.0412011 < p < 0.1587989
Using a point estimate and a margin of error, an interval
estimate of a population parameter such as µ can be constructed.
This interval estimate is called a confidence interval. For a
sample size n = 100 , confidence level of 95% and number of
success x = 10. Using Statdisk, the margin of error is obtained
and the probability that the confidence interval contains the
population proportion which is 95%
12
Conclusion
Importance of Distributions
Confidence Interval and Levels
Means and Variance
Use of Point Estimate
Critical Value
Margin of Error

10. We will recap on what the presenters discussed.
Normal distribution was defined and an example was shown
why this step is important. As the presenter shares the
measurements of the bears scientist can tell how old and how
the bears are growing (healthy or not).
The presenter explained the standard normal distribution and
how it is a bell shaped representation of data. He showed how
the normal distribution has varying levels of standard deviations
with stipulations.
The confidence intervals have many jobs. Earlier the presenters
discussed the standard normal distribution; this section is going
to discuss how a confidence interval is an interval, calculated
from the sample data that is very likely to cover the unknown
mean, variance, or proportion.
The confidence interval is discussed when the population mean
is not known. This information will assist in the life science of
bears can tell us on the weight, heights and other measurements
of the bears.
The confidence intervals have many jobs. Earlier the presenters
discussed the standard normal distribution; this section is going
to discuss how a confidence interval is an interval, calculated
from the sample data that is very likely to cover the unknown
mean, variance, or proportion.
The presenter discussed what a point estimate is. A brief
example of how a point estimate is found in a confidence
interval of bears. A bear article shows in details how the
researchers used point estimate along with other estimates.
Confidence level was defined with an example of how to find an
interval estimate.
Critical value is defined as the value for which a certain
percentage at a tail is true. The presenter showed an example
and explained how to calculate the critical value.
The margin of error was explained with using a point estimate,
and an interval estimate of a population parameter such as µ can

11. be constructed. The presenter has passed out more information
and a larger picture of the Statdisk information for the audience
to see what the presenter is discussing.
13
References (ALL)
Admin. (2006) Six Sigma Tutorial, Confidence Interval.
Retrieved October 3, 2011 from http://sixsigmatutorial.com/six-
sigma-confidence-intervals-tutorial/411/
Harris, R. B., White, G. C., Schwartz, C. C., & Haroldson, M.
A. (2007). Population growth of Yellowstone grizzly bears:
uncertainty and future monitoring. Ursus, 18(2), 168-178.
Retrieved from EBSCOhost.
lbowen11235. (2010, October 22). Theory of Normal
Probability Calculations Using the Standard Normal Table
[Video file]. Retrieved from YouTube website:
http://www.youtube.com/watch?v=zCormwRIP9s
Psomas, N. (2003).Chapter 6 Point Estimation. Retrieved
October 1, 2011, from
http://www.marin.edu/~npsomas/Lectures/ch6_confidence_inter
vals.htm
Triola, M. M., & Triola, M. F. (2006). Biostatistics for the
biological and health sciences. Boston, MA: Addison
Wesley/Pearson.
14