An occupant - traffic study was conducted to aid in the remodeling of an office building that contains three entrances. The choice of entrance was recorded for a sample of 150 people who entered the building, and is shown in the table below. Entrance 1 2 3 Number of 48 62 40 people entering Expected frequency Do the data indicate that there is a difference in preference for the three entrances? Test appropriate hypothesis at a = 0.05 a. State null hypothesis and alternative hypothesis. (0.5 mark) H: b. Find expected frequencies. Leave two digits after decimal point in the expressions for expected frequencies. (0.5 mark) c. State the calculated value of test statistic. (1 mark) d. State the critical value of the test (1 mark) Xer. = e. Decide whether null hypothesis is true and make the conclusion whether the data indicate that there is a difference in preference for the three entrances. (1 mark)