It is imperative that I restore productivity via a secret naturally-occurring mo

Question

It is imperative that I restore productivity via a secret naturally-occurring molecule, caffeine........

In order to see if my secret molecule works, I have observed the time, in hours, a random selection of ten of my colleagues

1.9

0.8

1.1

0.1

-0.1

4.4

5.5

1.6

4.6

3.4

What is a 95% confidence interval for the time my colleagues can stay awake on average for all of my colleagues?

Was my secret molecule effective in increasing their attention span, I mean, staying awake? And, please explain....

1.9

0.8

1.1

0.1

-0.1

4.4

5.5

1.6

4.6

3.4

Explanation / Answer

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)=2.33
Standard deviation( sd )=2.0022
Sample Size(n)=10
Confidence Interval = [ 2.33 ± t a/2 ( 2.0022/ Sqrt ( 10) ) ]
= [ 2.33 - 2.262 * (0.633) , 2.33 + 2.262 * (0.633) ]
= [ 0.898,3.762 ]

Yes, molecule was effective in increasing their attention, since 95% Cl is entirely to the right of zero.

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