# How to Calculate the Population Proportion in Excel – 3 Steps

Consider the problem below:

3 out of 100 New Yorkers have red hair. Construct a 90% confidence interval for the proportion of red haired people in the State of New York.

### Step 1 – Calculate the Sample Proportion

The Sample Proportion is the part of a given sample of individuals in larger group that follows a specific characteristic.

The parameter p′ represents the sample proportion and is used to calculate the genuine population proportion.

• The following equation is used to find the sample proportion:
p′=x/n
• p′ = the sample proportion
• x = the number of the sample population that meets the criteria
• n = the whole number of the sample population

Sample Proportion Calculation:

x = 3; n= 100

Now, p′ = x/n

p′ = 3/100

p′ = 0.03

### Step 2 – Calculate the Margin of Error

The Margin of Error is a value that estimates the percentage of sample points that can differ from real values.

• The formula to calculate the Margin of Error is:

• E= Margin of Error
• Zc= Critical Value
• p′= the sample proportion
• n= the whole number of the sample population

Critical Values represent the rejection region of a hypothesis test.

The following image shows critical values for different confidence intervals.

• To choose the correct Zc value from the list, use the following formula in C6.
`=INDEX('Sample Data'!B11:C15,MATCH(C5,'Sample Data'!B11:B15,0),2)`
• Calculate the Margin of Error by using the following formula:
`=C5*SQRT(C4*(1-C4)/C6)`

### Step 3 – Calculate the Population Proportion

• Taking the Margin of Error into account, the following equation will represent the population proportion with a confidence interval:
(p′-E)< P <(p′+E)
• As the Margin of Error is 0.0281, we get the left and right boundary of population proportion as shown below:

p′- E = 0.03 + 0.0281 =0.0581

p′+ E= 0.03 – 0.0281=0.0019

From the above inequality, we can conclude that the population proportion of redheads among the people in the New York State will be between 5.81% to 0.19%.

The normal distribution is shown in the image below. The population proportion will range between 0.19% to 5.81% for a confidence level of 90%. So, the range of population proportion for our sample problem will be:

0.0019 < P < 0.0581

Or,

0.19% < P < 5.81%

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Al Ikram Amit

Al Ikram Amit, holding a BSc in Naval Architecture & Engineering from Bangladesh University of Engineering and Technology, serves as a key Excel & VBA Content Developer at ExcelDemy. Driven by a profound passion for research and innovation, he actively immerses himself in Excel. In his role, Amit not only skillfully addresses complex challenges but also exhibits enthusiasm and expertise in gracefully navigating tough situations, emphasizing his steadfast commitment to consistently delivering exceptional, high-quality content that adds significant... Read Full Bio

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