Question

given a random sample of 50 measurements of acid levels in the water on one day recorded a sample mean of 210 with a standard deviation of 55. Create a 95% confidence interval for the parameter.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 210

Population standard deviation =    = 55

Sample size n =50

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z / 2   = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96 * (55 / 50 )

= 15.2
At 95% confidence interval
is,

- E < < + E

210- 15.2 <   < 210+ 15.2

194.8 <   <225.2