Answer:
20 +/- $6.74
= ( $13.26, $26.74)
The 90% confidence interval for the difference in average amounts spent on textbooks (math majors - English majors) is ( $13.26, $26.74)
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.
x1-x2 +/- margin of error
x1-x2 +/- z(√(r1^2/n1 + r2^2/n2)
Given that;
Mean x1 = $200
x2 = $180
Standard deviation r1 = $22.50
r2 = $18.30
Number of samples n1 = 60
n2 = 40
Confidence interval = 90%
z(at 90% confidence) = 1.645
Substituting the values we have;
$200-$180 +/-1.645(√(22.5^2/60 +18.3^2/40)
$20 +/- 6.744449847374
$20 +/- $6.74
= ( $13.26, $26.74)
The 90% confidence interval for the difference in average amounts spent on textbooks (math majors - English majors) is ( $13.26, $26.74)
