1.Most analysts focus on the cost of tuition as the way to measure the cost of a college education. But incidentals, such as textbook costs, are rarely considered. A researcher at the University of Macau (UM) wishes to estimate the textbook costs of first-year students at UM. To do so, she monitored the textbook cost of 250 first-year students and found that their average textbook cost was $900 per semester.

a.Identify the population of interest to the researcher.

b.Identify the variable of interest to the researcher. Is the variable numerical or categorical?

c.Identify the sample in the study.

d.Is the value $900 a parameter or a statistic? Explain.

2.The record of a corporation shows that, on average, accounts payable are $125.32. An auditor checked a random sample of 16 of these accounts. The sample mean and standard deviation were found to be $131.78 and $15.41 respectively. Assume the population distribution is normal. Is there evidence that the mean amount of all accounts payable in the corporation is different from the record of $125.32?

a.Write down the null and alternative hypotheses in this test.

b.What is the appropriate test probability distribution? Give the required condition(s) for using this distribution.

c.At 5% significance level, state the decision rule for the auditor to test the hypotheses.

d.Compute the value of the test statistic.

e.Based on the decision rule in part (c) only, what is the statistical decision?

f.Provide a conclusion about the amount of the accounts payable to the auditor.

3.The probability that a freshman passes the course Business Statistics in the first academic year is estimated to be 0.74. The probability that a freshman passes the course Probability in the first academic year is estimated to be 0.25. The probability that a freshman passes the course Business Statistics or the course Probability in the first academic year is estimated to be 0.89.

a.Are passing Business Statistics and passing Probability in the first academic year mutually exclusive? Explain statistically.

b.Are passing Business Statistics and passing Probability in the first academic year independent? Explain statistically.

c.What is the probability that a freshman will pass Business Statistic but not Probability in the first academic year?

d.What is the probability that a freshman will pass neither Business Statistics nor Probability in the first academic year?