Answer:
$16,341< μ <$22,459.
Step-by-step explanation:
The formula for calculating confidence interval is expressed as;
CI = xbar±(z×s/√n)
xbar is the mean tuition
z is the z score at 90% CI
s is the standard deviation
n is the sample size
Given
xbar = $19,400
s = $11,000
n = 35
z = 1.645
Substitute into the formula for calculating confidence interval
CI = xbar±(z×s/√n)
CI = 19400±(1.645×11000/√35)
CI = 19400±(1.645×11000/5.916)
CI = 19400±(1.645×1859.36)
CI = 19400±3058.65
CI = [19400-3,058.65, 19400+3,058.65]
CI = [16,341.35, 22,458.65]
CI = [16,341, 22,459] to nearest whole number.
Hence a 90% confidence interval for the mean tuition for all colleges and universities is 16,341< μ <22,459.
