A random sample of 15 property values has been drawn and is the following:

Sample-Size 15

375,000

327,000

669,000

379,500

420,000

550,500

240,000

370,500

1,077,000

478,950

720,000

532,500

257,580

360,000

255,000

Question:

Use this sample to test the population mean. Use the critical value and the p-value approach and a 5% level of significance. Assume that the population standard deviation is unknown, and the shape of the population property assessment values follows Normal distribution. Make sure to include all the steps of hypotheses (hypotheses, decision zone, critical value, p-value, conclusion with justification) and show your manual calculations.