Question

Fission tracks are trails found in uranium-bearing minerals, left by fragments released during fission events. An article reports that fifteen tracks on one rock specimen had an average track length of 11 μm with a standard deviation of 2 μm. Assuming this to be a random sample from an approximately normal population, find a 99% confidence interval for the mean track length for this rock specimen. Round the answers to three decimal places.

The 99% confidence interval is

Answer 1

solution

Given that,

$\bar x$ = 11

s =2

n =15

Degrees of freedom = df = n - 1 =15 - 1 =14

At 99% confidence level the t is ,

$\alpha$ = 1 - 99% = 1 - 0.99 = 0.01

$\alpha$ / 2 = 0.01 / 2 = 0.005

t$\alpha$ /2  df = t0.005,14 = 2.977    ( using student t table)

Margin of error = E = t$\alpha$/2,df * (s /$\sqrt$n)

= 2.977* (2 / $\sqrt$ 15) = 1.537

The 99% confidence interval estimate of the population mean is,

$\bar x$ - E < $\mu$ < $\bar x$ + E

11 - 1.537< $\mu$ < 11+ 1.537

9.463 < $\mu$ < 12.537

( 9.463 , 12.537)