Question

What is the 95% CI for data set 2?

data points - 10, 20, 30

n = 3

mean = 20

s = 10

SEM = 5.77

2SEM = 11.54

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Answer 1

Answer: 20 ± 11.32

Explanation: Confidence Interval (CI) is an interval of values where there is a % certainty the true mean value lies in. For example, a 95% CI means there is a 95% certainty the true mean value lies in the interval.

For the data set 2, z-value for 95% confidence interval is z = 1.96

Formula to calculate CI is

x ±
`z(s)/(√(n) )`

where

x is mean

z is z-value

s is standard deviation

n is the sample number

Then:

20 ±
`1.96(10)/(√(3) )`

20 ±
`1.96(10)/(1.7320)`

20 ±
`(19.6)/(1.7320)`

20 ± 11.32

The 95% CI is 20 ± 11.32, which means there is a 95% certainty the true value is between 8.68 and 31.32.