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Confidence Interval Formula Online - Tutorpace

# Confidence Interval Formula

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Confidence interval formula is a useful tool to find the range within which most values would occur. This
confidence interval is calculated after setting the confidence level. The confidence level in percentage,
mostly set at 95%. Which means 95% of the values will fall within the range for a specific outcome. The
confidence interval formula is given as
When n greater than or equal to 30 then confidence interval = x +-za/2(σ/√n)
But when n is less than 30 then the formula is confidence interval = x +-ta/2 (σ/√n)
a = 1 - (confidence level/ 100)

Example 1: In an exam 30 students obtained 20 average scores. The standard deviation is 10.

What will be the confidence level at 95% level?

Solution: In the given problem

N= 30, x = 20, std deviation = 10, level = 0.95 and a = 1 – (95/100) = 0.05

Plug in the values into the formula

Confidence interval = 20 +-ta/2 (10/√30)

20 +- 2.09302 (10/5.477) = 20 +- 3.821 = 16.178 to 23.821

The confidence level at 95% level16.178 to 23.821

Example 2: A website was visited by 25 people with number of average likes 10. The standard

deviation is 5. What will be the confidence level at 95% level?

Solution: In the given problem

N= 25, x = 10, std deviation = 5, level = 0.95 and a = 1 – (95/100) = 0.05

Plug in the values into the formula

Confidence interval = 10 +-ta/2 (5/√25)

10 +- 2.09302 (5/5)

10 +- 3.821 = 6.178 to 13.821

The confidence level at 95% level 6.178 to 13.821