Question

(23 pts. total) Past experience at Ziggog Travel Agency indicated that 56% of their clients wanted to go to Europe. During the most recent busy season, a sample of 1,000 clients were selected at random and was found that 548 of them were interested in a vacation in Europe. Ziggog management is interested in understanding if there has been a decrease in the percentage of people who want to travel to Europe. Conduct hypothesis testing (with a significance level of 0.05) through the following parts (parts a through g):

a) State the null hypothesis and the alternative hypothesis. (5 pts)

b) Find the sample proportion p. (3 pts)

c) Find the test statistic (calculated) z value by using the z= p-π/(√π(1-π)/n), (5 pts)

d) Draw the normal curve, then plot the critical z and test statistic z. (use critical z-value of 1.65. Determine + and/or – sign according to test type: 2-tailed or 1 tailed, and then if 1 tailed, left or right tailed) (4 pt) e) Make a decision about the null hypothesis: do you reject it or fail to reject it? State the decision and briefly explain why you made the decision. Interpret the decision within the context of the problem. (6 pts)

Answer 1

we have :- Past Experience at ziggog Travel Agency clients wanted to go to indicated that 56% of their Europe. te P=.56%.=10.56] n = 1000 clients ¢ x= 548 were interested in a vacation in Europe. ipse = 548 -0.548| 1000 claim : ziggog management is interested in if if there there understanding has been has been a a d decrease in the percentage of people who want to travel to Europe

level of significance Ed= 0.05. state null & alternative hypothesis: Ho: a = 0.56 vs H, T20.56. sample proportion = e = x = 10.548 - Test statishic = or *(1-0)

2= 10.548 - 0.56) -0.012 -1-0.764 0.01569 1 0.56*0.44 1000 @ normal curve critical a value +1 -1.647 Acceptance - Region C -1.64 0.764 Test statiche Rejection Region (from tables Cour test is left tailed hence critical value should be negative according to test tupe : one failed (left)

Decision 2 :- we reject Ho at Cl-d)X100 % level of significance if -2 stat <-za here - zstad 7-2 we fail to reject Hol at a=0.05. conclusion : There is not sufficient, evidence to conclude that there has been a decrease in the percentage of people who want to travel to Europe at = 0.05 level of significance.