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 )

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25 23 26
28 24
21 26 24
25 27
Mean = 24.9 ; Standard Deviation = 2.0248
Find a 90% confidence interval for the weights of the 3-in-1
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1
819500
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3
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4
220000
5
110000
6
499999
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