In: Statistics and Probability
In a random sample of 23 people, the mean commute time to work was 31.2 minutes and the standard deviation was 7.3 minutes. Assume the population is normally distributed and use a t-distribution to construct a 98% confidence interval for the population mean μ. What is the margin of error of μ? Interpret the results.
Solution :
Given that,
Point estimate = sample mean =
= 31.2
Population standard deviation =
= 7.3
Sample size = n =23
At 98% confidence level the z is ,
= 1 - 98% = 1 - 0.98 = 0.02
/ 2 = 0.02/ 2 = 0.01
Z/2 = Z0.01 = 2.326 ( Using z table )
Margin of error = E = Z/2
* (
/n)
= 2.326 * ( 7.3/ 23
)
= 3.54
At 98% confidence interval estimate of the population mean
is,
- E <
<
+ E
31.2 - 3.54 <
< 31.2+ 3.54
27.66 <
< 34.74
(27.66 , 34.74)