Question

# The Sumatra tiger is an endangered subspecies of the tiger, endemic to The island of Sumatra....

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).

#### Homework Answers

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 )

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