Question

Question 3) Suppose that El Camino is studying the cost of textbooks for college students. Accord- ing to research from 2013 a college students spends 655 dollars per year on textbooks. El Camino wants to study if recent trends such as e-books, online notes, bundled custom editions ete have reduced this cost for their students. To do this they take a random sample of 31 current students and find that the average student spent 595 dollars with a standard deviation of 280 dollars. (Note: You may assume there are approximately 20,000 El Camino students). (a) Carry out a hypothesis test at a = .05 to test the claim that recent trends have reduced the average cost of textbooks for El Camino students. Make sure to check all necessary conditions and state your conclusion in the context of this situation. (b) Describe what it would mean in this situation to make a Type I error (c) Describe what it would mean in this situation to make a Type II error EXTRA CREDIT QUESTION: Look back at Question 2. What is the probability that for four weeks in a row the food truck makes more than 5600 dollars in total revenue each week?

Answer 1

a)

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: 655 На: д < 655 This corresponds to a left-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used. (2) Rejection Region Based on the information provided, the significance level is a 0.05, and the critical value for a left- tailed test is te = -1.697 The rejection region for this left-tailed test is R t t < -1.697 (3) Test Statistics The t-statistic is computed as follows: 595 655 -1.193 t s//n 280//31 S (4) Decision about the null hypothesis Since it is observed that t -1.193 > te = -1.697, it is then concluded that the null hypothesis is not rejected Using the P-value approach: The p-value is p 0.1211, and since p 0.1211 0.05, it is concluded that the null hypothesis is not rejected. (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean u is less than 655, at the 0.05 significance level.

b)

type i error - reject the null hypothesis when it is true

it means that we conclude that cost of textbooks have reduced when it is not the case.

c)

type ii error - fail to reject the null hypothesis when it is false

it means that we fail to conclude that the cost of textbooks have reduced when it is actually true