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Mathematics & Economics
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Topic:

The Confidence Interval for the Population Proportion

Essay Instructions:

Sample statistics, such as the sample mean or the sample proportion, can be used to estimate a population parameter (such as the population mean or the population proportion). For example, you can estimate the true mean weight of all full-term newborn babies in the entire world by collecting a sample and using that sample to generate a 95% confidence interval.
Because the sample is a relatively small portion of the entire population, errors will have to be considered. Using a sample to create a range or interval of values that estimates a population value is called a “confidence interval.”
The general “confidence interval” formula is:
(sample statistic – E) < population parameter < (sample statistic + E)
To calculate a confidence interval, the margin of error (E) must first be calculated.
The margin of error, E, for means is: E=1.96sn√ where s is the sample standard deviation and n is the sample size.
The margin of error, E, for a 95% confidence interval for proportions is: E=1.96pˆ(1−pˆ)n−−−−−√ where pˆ is the sample proportion and n is the sample size.
UPDATE :
the writer can invent the values for sample proportion and sample size to compute the margin of error. After that, he can check on the internet the formula to calculate the 95% confidence interval.

Essay Sample Content Preview:

Statistics
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It is often impossible to establish the actual values of population parameters since it is difficult to collect data from the entire population. Therefore, researchers make conclusions about the general population based on information from the sample. Mostly, their main objective is to estimate population parameters such as µ and p based on sample data (McLeod, 2019). Sample estimates are seldom equal to the actual population value; they may be lower or higher than the population value. It is useful to know how wide the error in estimating the parameters is likely to be. The purpose of confidence intervals is to provide information about the uncertainty of these estimates.
A confidence interval consists of a range of values within which the unknown population parameter is expected to lie. It is an interval estimate of a population parameter established using sample data and a certain confidence level (Bluman, 2017). A confidence interval measures how well the sample being used represents the population being studied.
Suppose that in a sample of 30 patients who have received the Covid-19 vaccine, 18 of them are males. We will establish a 95% confidence interval for the true proportion of males who have received the COVID-19 vaccination. The table below shows the data of the 30 vaccinated patients.
Vaccinated Patients No.

Patient’s Gender

001

Female

002

Male

003

Male

004

Male

005

Male

006

Male

007

Male

008

Male

009

Updated on
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