5 SIx measurements were made of the mineral content in perce

5. SIx measurements were made of the mineral content (in percent) of spinach, with the following results. It is reasonable to assume that the population is approximately normal. 19.1, 20.1, 20.8, 19.7, 20.5, 21.8. Find the lower bound of the 95% confidence interval for the true mineral content. Round your answer three decimal places.

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)=20.33
Standard deviation( sd )=0.9352
Sample Size(n)=6
Confidence Interval = [ 20.33 ± t a/2 ( 0.9352/ Sqrt ( 6) ) ]
= [ 20.33 - 2.5706 * (0.382) , 20.33 + 2.5706 * (0.382) ]
= [ 19.349,21.311 ]