A random sample of 10 college students has a mean earnings of $3120 with a sample standard deviation of $677 over the summer months. Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be used to test a claim: μ > $3000.

t-distribution should be used to test a claim : μ > $3000.

Step-by-step explanation:

We are given that a random sample of 10 college students has a mean earnings of $3,120 with a sample standard deviation of $677 over the summer months.

We have to test a claim of μ > $3,000.

Since in this question we are provided with;

Sample mean earnings, = $3,120

Sample standard deviation, s = $677

Sample of college students, n = 10

So, Null Hypothesis, : $3,000

Alternate Hypothesis, : > $3,000

The distribution that we will use here for our test statistics will be t-distribution because in the question we don't know anything about population standard deviation .

Normal distribution is used when we know population standard deviation .

So, the test statistics used will be One-sample t-test statistics;

        Test statistics = ~

Therefore, t-distribution should be used to test a claim: μ > $3000.