Question

The average student loan debt amongst households in Oregon is $8,400. A hypothesis test is to be performed to test whether the mean student loan debt for households in Portland, OR, is the same as the mean student loan debt for the state of Oregon. Collecting data for sample of 31 households yielded a sample mean student loan debt of $9,800 and sample std. dev. of $4,700. Use sig. level of α = 0.05.

(a) State the Hypothesis to be tested.

(b) Compute the appropriate test statistic.

c) Obtain the appropriate critical value.

(d) Carefully state the conclusion from the hypothesis test.

Answer 1

Answer:

Given that:

Collecting data for sample of 31 households yielded a sample mean student loan debt of $9,800 and sample std. deviation of $4,700. Use significance level of α = 0.05.

(a) State the Hypothesis to be tested.

To test the hypothesis, The null hypothesis and Alternative hypothesis

(b) Compute the appropriate test statistic.

Test statistics: is unknown

(c) Obtain the appropriate critical value.

The critical value

Using t-table df=n-1=30

The critical values are

(d) Carefully state the conclusion from the hypothesis test.

Here

We fail to reject the null hypothesis

There is sufficient evidence to support the claim that the average student loan debt amongst households in Oregon is 8400