To study the metabolism of insects researchers fed cockroach

To study the metabolism of insects, researchers fed cockroaches measured amounts of a sugar solution. After 2, 5, and 10 hours, they dissected some of the cockroaches and measured the amount of sugar in various tissues. Five roaches fed the sugar D-glucose and dissected after 10 hours had the following amounts (in micrograms) of D-glucose in their hindguts:

Amounts of D-glucose 55.95 68.24 52.73 21.5 23.78

The researchers gave a 95% confidence interval for the mean amount of D-glucose in cockroach hindguts under these conditions. The insects are a random sample from a uniform population grown in the laboratory. We therefore expect responses to be Normal.

The mean (±0.01) and the standard deviation (±0.0001) of the SRS are:   

Xbar = s=

The critical value (±0.001) from the distribution for 95% confidence interval is:   
t* =

What confidence interval (±0.01) did the researchers give? ___ to ___ .

Solution

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)=44.44
Standard deviation( sd )=20.741
Sample Size(n)=5
Confidence Interval = [ 44.44 ± t a/2 ( 20.741/ Sqrt ( 5) ) ]
= [ 44.44 - 2.776 * (9.276) , 44.44 + 2.776 * (9.276) ]
= [ 18.691,70.189 ]