Question

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?

Answer 1

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

Step-by-step 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:

`\bar x=(1)/(n)\sum X=(1)/(10)* 213537=21353.70`

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

Compute the test statistic value as follows:

`z=(\bar x-\mu)/(\sigma/√(n))=(21353.70-27200)/(5000/√(10))=-3.70`

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:

`p-value=P(Z>-3.70)=P(Z<-3.70)=0.00011`

*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.