In: Statistics and Probability
A random group of 50 bowlers had an average score of 189. The standard deviation of all bowlers in the league was 9.1. Assume the population has a normal distribution. Find the margin of error, and then find the 95% confidence interval for the population mean
Solution :
Given that,
Point estimate = sample mean = = 189
Population standard deviation = = 9.1
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* ( 9.1 / 50 )
Margin of error = E = 2.5224
At 95% confidence interval estimate of the population mean
is,
- E < < + E
189 - 2.5224 <
<189 + 2.5224
186.4776<
< 191.5224
( 186.4776, 191.5224)