Confidence Interval and Estimation
Estimation
In statistics when we refer to the estimation we refer to the process that help us to make
conclusions about the population based on the information that we take from a sample.
For example: Let us assume that we want to estimate the mean heart rate of the
American citizens. That is impossible because the American population is
approximately 325 million citizens. So what do we do instead; we take a random
sample of American citizens and we measure the heart rate of the random sample. Then
we can calculate the sample heart rate mean 𝑋̅. From the sample mean we can estimate
the population heart rate mean 𝜇. An estimation of the population parameter can be
expressed by two ways. There are two different types of estimates. The point estimate
and the interval estimate. With the point estimate you end up with one single number
for the parameter that you are looking for. With interval estimates you are going to
have a range of values that represent the parameter that you are looking of.
In statistics we prefer to report an interval of reasonable values based on a sample,
rather than a single value. This interval of reasonable values is called an interval
estimator. The interval estimator of the population is called the confidence interval.
Confidence interval
Due to the fact that the sample is a selection of objects from the population it will never
be a perfect representation of the population. Different samples from the same
population will give different results. This is called a sampling error. For this reason
Statistics I / MTH 2000
, we use the confidence interval. A Confidence interval measures the probability that a
requested population parameter will lie between two specific values. Confidence
interval can take any value of probability from 0-100% but the most common are the
90%, 95% and 99% [1]. For more accuracy in our estimation high level of confidence
interval is required.
Calculation of the Confidence interval(CI)
For the calculation of the Confidence interval of the sample the following steps should
be followed:
Step1: Define the sample size 𝑛, calculate the mean 𝑋̅(sampling distribution of the
mean) and standard deviation 𝜎.
Step 2: Decide what confidence level we want to use(90%,95%,99% etc.) and based
on the table below find the ‘𝑧’ value for the specific confidence interval.
Statistics I / MTH 2000
Estimation
In statistics when we refer to the estimation we refer to the process that help us to make
conclusions about the population based on the information that we take from a sample.
For example: Let us assume that we want to estimate the mean heart rate of the
American citizens. That is impossible because the American population is
approximately 325 million citizens. So what do we do instead; we take a random
sample of American citizens and we measure the heart rate of the random sample. Then
we can calculate the sample heart rate mean 𝑋̅. From the sample mean we can estimate
the population heart rate mean 𝜇. An estimation of the population parameter can be
expressed by two ways. There are two different types of estimates. The point estimate
and the interval estimate. With the point estimate you end up with one single number
for the parameter that you are looking for. With interval estimates you are going to
have a range of values that represent the parameter that you are looking of.
In statistics we prefer to report an interval of reasonable values based on a sample,
rather than a single value. This interval of reasonable values is called an interval
estimator. The interval estimator of the population is called the confidence interval.
Confidence interval
Due to the fact that the sample is a selection of objects from the population it will never
be a perfect representation of the population. Different samples from the same
population will give different results. This is called a sampling error. For this reason
Statistics I / MTH 2000
, we use the confidence interval. A Confidence interval measures the probability that a
requested population parameter will lie between two specific values. Confidence
interval can take any value of probability from 0-100% but the most common are the
90%, 95% and 99% [1]. For more accuracy in our estimation high level of confidence
interval is required.
Calculation of the Confidence interval(CI)
For the calculation of the Confidence interval of the sample the following steps should
be followed:
Step1: Define the sample size 𝑛, calculate the mean 𝑋̅(sampling distribution of the
mean) and standard deviation 𝜎.
Step 2: Decide what confidence level we want to use(90%,95%,99% etc.) and based
on the table below find the ‘𝑧’ value for the specific confidence interval.
Statistics I / MTH 2000
