The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor’s degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The α is set to 0.05. The confidence interval for this hypothesis test would be __________________.
Multiple Choice
[$16,279.7, $17,720.3]
[$14,839.1, $19,160.9]
[$16,788.22, $19,611.78]
[$14,118.9, $19,881.2]
Here
a = 0.05 so confidence level c = 0.95
Also population standard deviation is given
We have to find 95% confidence interval for population mean
xbar - Za/2*(/√n) < < xbar + Za/2*(/√n)
For a = 0.05 , Za/2 = Z0.025 = 1.96
18200 -1.96*(4200/√34) < < 18200+1.96*(4200/√34)
16788.22 < < 19611.78
So the required confidence interval is [16788.22, 19611.78]
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