In: Statistics and Probability
Eight chemical elements do not have isotopes. A random sample of 30 of the elements that do not have isotopes showed a mean number of 19.63 isotopes per element and the population has a standard deviation of 18.73. Estimate the true mean number of isotopes for all elements with isotopes with 90% confidence. (5 pts) How would I solve this? What formula would I use?
Solution :
Given that,
Point estimate = sample mean = = 19.63
Population standard deviation =
= 18.73
Sample size = n = 30
At 90% confidence level the z is
= 1 - 90% = 1 - 0.90 = 0.1
/ 2 = 0.1 / 2 = 0.05
Z/2 = Z0.05 = 1.645 ( Using z table )
Margin of error = E = Z/2
* (
/n)
=1.645 * ( 18.73 / 30 )
= 5.6253
At 90% confidence interval estimate of the population mean
is,
- E <
<
+ E
19.63 - 5.6253 <
< 19.63 + 5.6253
14.0047 <
< 25.2553
( 14.0047 25.2553)