In: Statistics and Probability
we want to build a 95% confidence interval for the average height of Swedes. 48 Swedes are surveyed. The average of the sample is 71 inches. The standard deviation of the sample is 2.8 inches. indicates the upper limit of the interval
The formula for confidence interval estimation is:
μ = M ± t(sM)
where:
M = sample mean
t = t statistic determined by confidence
level
sM = standard error =
√(s2/n)
M = 71
t = 2.01
sM = √(2.82/48) = 0.4
μ = M ± t(sM)
μ = 71 ± 2.01*0.4
μ = 71 ± 0.81
95% CI [70.19, 71.81].
Lower Limit=70.19
Upper limit=71.81
t score at 47 degree of freedom calculated using t-table shown below as