Question

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?

Answer 1

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)