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To estimate the mean length of rattlesnakes, 10 such snakes are randomly selected. Their lengths, in inches, are as follows: 40.2 43.1 45.4 44.5 39.5 40.2 41.0 41.6 43.1 44.9 Find a 90% confidence interval for the mean length of all rattlesnakes.

Sagot :

Cricetus

Answer:

The confidence interval will be "41.04, 43.81".

Step-by-step explanation:

Given that,

Sample size,

n = 10

Sample total,

423.5

Sample mean,

[tex]\bar X =\frac{423.5}{10}[/tex]

   [tex]=42.35[/tex]

Sample variance,

[tex]s = \sqrt{4.5894}[/tex]

  [tex]=2.1423[/tex]

[tex]df=n-1[/tex]

   [tex]=9[/tex]

[tex]t^*=18331[/tex]

Now,

The margin of error will be:

⇒ [tex]E=\frac{s\times t^*}{\sqrt{n} }[/tex]

       [tex]=\frac{2.1423\times 1.8331}{\sqrt{9} }[/tex]

       [tex]=\frac{3.928}{3 }[/tex]

       [tex]=1.309[/tex]

hence,

The 90% confidence level will be:

= [tex](\bar X-E),(\bar X+E)[/tex]

By substituting the values, we get

= [tex](42.35-1.309),(42.35+1.309)[/tex]

= [tex](41.04),(43.81)[/tex]

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