Open the Undergrad Debt data in the Excel file. Nationally, on average, a college student last year graduated with $27,200 in debt with a historical standard deviation of $5,000. The file gives sample date from Arkansas. Does Arkansas students have higher debt than the national average at alpha equal to 10?

Arkansas students have higher debt than the national average, $27,200.

Explanation:

The provided data is:

S = {24040, 19153, 26762, 31923, 31533, 34207, 14623, 24370, 31016}

In this case we need to test whether Arkansas students have higher debt than the national average at alpha equal to 0.10.

The hypothesis can be defined as follows:

H₀: Arkansas students does not have higher debt than the national average, i.e. μ ≤ $27,200.

Hₐ: Arkansas students have higher debt than the national average, i.e. μ > $27,200.

Compute the sample mean:

As the population standard deviation is provided, we will use a z-test for single mean.

Compute the test statistic value as follows:

The test statistic value is -3.70.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

Compute the p-value for the test as follows:

*Use a z-table for the probability.

The p-value of the test is 0.00011.

p-value = 0.00011 < α = 0.10

The null hypothesis will be rejected.

Thus, it can be concluded that Arkansas students have higher debt than the national average, $27,200.

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