A vending machine that dispenses coffee into cups must fill the cups with 7.8 oz of liquid. Before selling the vending machine to a college or business, the company tests the machine to be sure it is dispensing an average amount of 7.8 oz of coffee. A sample of 20 amounts is shown here. Assume that the amount of coffee dispensed is normally distributed. Ounces Dispensed 7.78 7.82 7.87 7.80 7.80 7.83 7.85 7.84 7.82 7.81 7.79 7.82 7.84 7.82 7.78 7.75 7.83 7.73 7.87 7.88 (a) Set up the null and alternative hypotheses to test whether average amount of coffee dispensed is different from 7.8 ounces. (b) Test the hypotheses from part (a) with a = 5% by computing a critical region and the p-value. Is there enough evidence to reject the null hypothesis? (c) Compute the p-value corresponding the hypotheses testing in part (a). What is your conclusion when a = 0.05. (d) Now use a = 0.1 for part (c). What is your decision?