Anaylysis of the venom of 7 eightdayold worker bees yielded

Anaylysis of the venom of 7 eight-day-old worker bees yielded the floowing observations on histamine content in nanograms: 649, 832, 418, 530, 384, 899, 755.

(a) Construct by hand a 90% CI for the true mean histamine content for all worker bees of this age. What assumptions, if any, are needed for the validity of the CI(Confidence Interval)?

(b) The true mean histamine content will be in the CI you constructed in part (a) with probability 90%. True or False?

Solution

a)
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)=638.143
Standard deviation( sd )=201.72
Sample Size(n)=7
Confidence Interval = [ 638.143 ± t a/2 ( 201.72/ Sqrt ( 7) ) ]
= [ 638.143 - 1.943 * (76.24) , 638.143 + 1.943 * (76.24) ]
= [ 490,786.28 ]
b)
True