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 amount (in micrograms) of D-glucose in their hindguts.

53.6   21.50    37.55    38.62 27.92

The researchers gave a 95% confidence 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. What confidence interval did the researchers give? (Use 2 decimal places.)
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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)=35.838
Standard deviation( sd )=12.19
Sample Size(n)=5
Confidence Interval = [ 35.838 ± t a/2 ( 12.19/ Sqrt ( 5) ) ]
= [ 35.838 - 2.776 * (5.45) , 35.838 + 2.776 * (5.45) ]
= [ 20.7,50.97 ]