Today you took a 19 randomly samples widget from your new pr

Today you took a 19 randomly samples widget from your new production line(which makes thousands a day) & measured dimension x. You ot the values listed below. You assume that the x is distributed normally in the population.

Sample mean=20.98 mm

Sample standard devitation= 0.75mm

Compute the 95% confidence interval for the population mean of dimension x

Solution

Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=20.98
Standard deviation( sd )=0.75
Sample Size(n)=19
Confidence Interval = [ 20.98 ± t a/2 ( 0.75/ Sqrt ( 19) ) ]
= [ 20.98 - 2.1009 * (0.172) , 20.98 + 2.1009 * (0.172) ]
= [ 20.619,21.341 ]