Answer:
$65,351+/-$3,661.73
= ( $61,689.27, $69,012.73)
Therefore, the 90% confidence interval (a,b) = ( $61,689.27, $69,012.73)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = $65,351
Standard deviation r = $7,711
Number of samples n = 12
Confidence interval = 90%
z(at 90% confidence) = 1.645
Substituting the values we have;
$65,351+/-1.645($7,711/√12)
$65,351+/-1.645($2,225.973962860)
$65,351+/-$3661.727168905
$65,351+/-$3,661.73
= ( $61,689.27, $69,012.73)
Therefore, the 90% confidence interval (a,b) = ( $61,689.27, $69,012.73)
