A transportation manager claims that over 86% of train travelers buy their tickets before boarding the train. Only a small number of people on the train will be checked on the train to see whether they bought a ticket before boarding. Suppose that information about a random sample of 504 train travelers was collected and 57 of them did not purchase a ticket before boarding.By answering the following question, test at the 5% significance level if the manager's claim is supported by the survey data.

Question 1

Letpdenote the proportion of train travelers who bought train tickets before boarding the train. The correct hypotheses are:

a) H0: p = 0.86 and H1: p > 0.86

b) H₀:p< 0.86 and H₁:p= 0.86

c) H₀:p= 0.86 and H₁:p< 0.86

d) H₀:p 0.11 and H₁:p> 0.11

e ) H₀:p< 0.11 and H₁:p> 0.11

Question 2

Assuming that the null hypothesis is true, what is the standard error of the sample proportion?

a) 0.0155

b) 0.4267

c) 0.4723

d) 0.0272

e) 0.0813

Question 3

The corresponding test statistic value is:

a) -1.009

b) 1.74

c) 1.047

d) 1.254

e) 1.001

Question 4

The critical value for the test is:

a) -1.28

b) -1.64

c) 1.96

d) 1.64

e) -2.33

Question 5

The decision and conclusion for this test are:

a) test statistic > critical value, thus H₀cannot be rejected. There is insufficient evidence supporting the manager's claim.

b) test statistic > critical value, thus H₀is rejected. There is enough evidence supporting the manager's claim.

c) test statistic < critical value, thus H₀is rejected. There is enough evidence supporting the manager's claim.

d) test statistic < critical value, thus H₀cannot be rejected. There is insufficient evidence supporting the manager's claim.

Question 6

The manager would like to estimate the proportion of travelers who buy their tickets before boarding the train using a 0.08 margin of error and a 10% significance level, what sample size should they use? Use the proportion of the customers who bought a ticket in advance from the information given in the above problem statement.

a) 96

b) 88

c) 56

d) 43

e)95