Question

The Sumatra tiger is an endangered subspecies of the tiger, endemic to The island of Sumatra. A researcher measures the length of the upper canine teeth of eight Sumatra tigers in mm, as recorded below.
25 28 24 26 23 27 23 25
Use this sample to determine the upper limit of a 95% confidence interval for the population mean length of the teeth (in mm).

Answer 1

Solution:

x	x2
25	625
28	784
24	576
26	676
23	529
27	729
23	529
25	625
∑x=201	∑x2=5073

Mean ˉx=∑xn

=25+28+24+26+23+27+23+25/8

=201/8

=25.125

Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√5073-(201)28/7

=√5073-5050.125/7

=√22.875/7

=√3.2679

=1.8077

Degrees of freedom = df = n - 1 = 8 - 1 = 7

At 95% confidence level the t is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,7 =2.365  

Margin of error = E = t/2,df * (s /n)

= 2.365 * (1.81 / 8)

= 1.51

Margin of error = 1.51

The 95% confidence interval estimate of the population mean is,

- E < < + E

25.12 - 1.51 < < 25.12 + 1.51

23.61 < < 26.63

(23.61, 26.63 )