To answer this question, let's use statistical hypothesis testing to compare the price of new graduates' salaries from University to the national average salary for new college graduates. We'll use the Z-test since we know the standard deviation and the sample size is large enough (n = 100).
1. State the hypotheses. The null hypothesis is that the university's graduates do not earn more than the average, while the alternative hypothesis is that the university's graduates earn more than the average salary.
2. Collect sample data. The sample mean (the average salary of university's graduates) is $53,200, the standard deviation is $20,400, and the sample size is 100.
3. Calculate the standard error. The standard error (SE) is a measure of how spread out the values within a data set are likely to be. It can be calculated by dividing the standard deviation by the square root of the sample size. From our data, SE = $20,400 / sqrt(100) = $2040.
4. Compute the Z-score. Z-score is a measure of how many standard errors a point is from the population mean. It is calculated as the difference between the sample mean and the population mean divided by the standard error. Using our data, Z = ($53,200-$50,556) / $2040 = 1.296.
5. Find the P-value. The P-value is the probability that you have falsely rejected the null hypothesis. It can be found using statistical tables which relate Z-scores to their corresponding P-values. In our case, the P-value corresponding to Z = 1.296 is approximately 0.097.
6. Interpret the results. If the P-value is less than the chosen significance level (often 0.05), that indicates strong evidence against the null hypothesis, so you reject the null hypothesis. In our case, the P-value is more than 0.05, hence there is not enough evidence to reject the null hypothesis.
Therefore, based on the data we have, there is not enough evidence to support the claim that the university's graduates earn more than the average salary.