Question

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.

Answer 1

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,

$\bar X =\frac{423.5}{10}$

   $=42.35$

Sample variance,

$s = \sqrt{4.5894}$

  $=2.1423$

$df=n-1$

   $=9$

$t^*=18331$

Now,

The margin of error will be:

⇒ $E=\frac{s\times t^*}{\sqrt{n} }$

       $=\frac{2.1423\times 1.8331}{\sqrt{9} }$

       $=\frac{3.928}{3 }$

       $=1.309$

hence,

The 90% confidence level will be:

= $(\bar X-E),(\bar X+E)$

By substituting the values, we get

= $(42.35-1.309),(42.35+1.309)$

= $(41.04),(43.81)$