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 $15,600. A random sample of 40 students had an average debt load of $16,800. It is believed that the population standard deviation for student debt load is $4,400. The α is set to 0.05. The confidence interval for this hypothesis test would be __________.
Question
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 16,800. It is believed that the population standard deviation for student debt load is $4,400. The α is set to 0.05. The confidence interval for this hypothesis test would be __________.
Solution
To calculate the confidence interval for this hypothesis test, we first need to calculate the standard error. The standard error (SE) is calculated by dividing the standard deviation by the square root of the sample size.
In this case, the standard deviation (σ) is $4,400 and the sample size (n) is 40.
SE = σ / √n = 4400 / √40 = 696.31
Next, we need to calculate the margin of error (ME). The ME is calculated by multiplying the standard error by the z-score associated with our desired confidence level.
For a confidence level of 95% (α = 0.05), the z-score is 1.96.
ME = SE * z = 696.31 * 1.96 = 1364.85
Finally, we calculate the confidence interval by adding and subtracting the margin of error from the sample mean.
The sample mean (x̄) is $16,800.
Confidence interval = x̄ ± ME = 16800 ± 1364.85 = [18,164.85]
So, the confidence interval for this hypothesis test would be [18,164.85].
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