A drug manufacturer in Malaysia is interested in the proportion of persons who

have depression whose condition can be controlled Y a new drug company has

developed. A study was conducted involving 6000 individuals with depression and

found that 80% of the individual are able to control their condition with the drug.

Assuming that 6000 individuals are representative of the group who have depression,

answer the following questions

a. What is the populations?

b. What is the sample?

c. Identify the statistic and give its value.

d. Do we know the value of the parameter? Why?

12. Suppose a random sample of size n = 100 has been selected and the sample mean

is found to be x = 67. The population standard deviation is assumed to be = 12.

Please answer the following questions.

(a) What is the standard error of the mean?

(b) What is the margin of error if the confidence level is (1 - ) = 0.95?

(c) What is the 95% confidence interval estimate of?

13. Suppose a random sample of size n = 36 has been selected from a population

with = 30 and a sample mean of x = 205

(a) What is the 90% confidence interval estimate of ?

(b) What is the 95% confidence interval estimate of ?

(c) What is the 99% confidence interval estimate of ?

(d) If a 99% confidence interval is [228, 232] for a population with = 10, what is n?

14. Provide the interval estimate at the 90% confidence level for each case below.

(a) For n = 40, the sample mean is x = 70; assume it is known that = 6.

(b) For n = 120, the sample mean is x = 44; assume it is known that = 2.

(c) For n = 81, the sample mean is x = 0; assume it is known that = 9.

(d) For n = 30, the sample mean is x = -12; assume it is known that = 7.

15. In a continuing study of the amount Pharmacy students are spending each term on

text- books, data were collected on n = 81 students. In previous studies, the population

standard deviation has been = RM24.

(a) What is the margin of error at the 99% confidence level?

(b) If the mean from the most recent sample was x = RM288, what is the 99%

confidence interval estimate of the population mean ?

16. Assume that the average financial endowment of Malaysian universities is

RM313,182, 000. If this estimate is developed on a random sample size of n = 30, what

is the 80% confidence interval estimate of the population mean ? Assume the

population standard deviation is = RM64, 500, 000.

17. Referring to the Question 16, if the data tend to be highly skewed because of the

presence of a dozen or so very wealthy universities, does the above procedure lead to

reliable estimates? If not, comment on what might be done to improve the estimation

procedure.

18. A sample of Petrol prices was taken at n = 70 service stations across Malaysia., and

the sample mean price per litre was found to be x= RM3.67, the sample standard

deviation s = RM0.21.

(a) What is the 90% confidence interval estimate of the population mean price per

litre ?

(b) What is the 95% confidence interval estimate of the population mean price per

litre ?

(c) What is the 99% confidence interval estimate of the population mean price per

litre ?

19. A survey finds that the average Malaysian household is expected to spend RM868

on holiday-related expenses during the next Raya period. This amount covers not only

gifts, but food, beverages, and decorations. Assume the study is based on n = 94

randomly sampled households throughout the Malaysia. Assume that the sample

standard deviation is s=RM162.

(a) What is the 60% confidence interval estimate of the population mean amount- to-be-

spent during the Raya holiday period?

(b) What is the 80% confidence interval estimate of the population mean amount- to-be-

spent during Raya holiday period?

(c) What is the 90% confidence interval estimate of the population mean amount- to-be-

spent during the Raya holiday period?

20. Accordingly to one of the Malaysia Statistical Department, the average net wealth of

those individuals classied as members of the (upper) 1% is RM8, 400, 000. If this value

was developed on a sample of size n = 20 individuals, can you see any problem using

the confidence interval estimate methods of you have learned with Dr. Adrian's class?

Discuss about that.

21. Suppose the Dean of a large medical college wishes to estimate the mean student

age of the most recent entering class of aspiring physicians pursuing an M.B.B.S.

degree. A quick pilot study reveals that 3 years might be used as an estimate of the

value of . If a 95% confidence interval estimate with a margin of error 1 is desired,

what sample size should we recommend?

22. The commute-to-work time for the residents of the world's large cities has been

investigated extensively. A pilot study involving a random sample of residents of Kuala

Lumpur is used to provide an estimate of = 10 minutes for the population standard

deviation.

(a) If we want to estimate the population mean commute-to-work time for the residents

of Kuala Lumpur with a margin of error of 2 minutes, what sample size n should we

recommend? Assume 90% confidence.

(b) If we want to estimate the population mean commute-to-work time for the residents

of Kuala Lumpur with a margin of error of 1 minute, what sample size n should we

recommend? Assume 90% confidence.

23. A sample of 64 MBA students at the Management and Science University (MSU)

reported they spent an average of RM252.45 on textbooks and case materials per

semester. Assume the population standard deviation is =RM74.50.

(a) What is the 95% confidence interval estimate for the mean amount spent per term

by an MBA student at MSU?

(b) How large a sample would be needed to estimate with a margin of error of RM10

at 90% confidence?

24. In a pilot study, n = 80 respondents have been interviewed, 56 of whom have

answered "yes" to a particular survey question. What sample size n is required if we

wish to estimate the population proportion p of "yes" answers with a margin of error of

0.02 at the 95% level of confidence?

25. Referring to the previous exercise, what sample size should we recommend if we

had no pilot study data to go on? Would n be greater or less than the n recommended in

the previous exercise? Assume the study is investigating a question never before

researched.

26. In a study of consumer confidence among middle-class Malaysian families, 450

were interviewed in the metropolitan area Kuala Lumpur. When asked about having to

cut back on discretionary purchases of big-ticket items, 212 of 450 responded that their

families had done so over the previous 6 months.

(a) What is the 90% confidence interval estimate of the population proportion p of this

type of household cutting back on discretionary spending?

(b) What sample size should we recommend to achieve a margin of error of 0.03?

27. Referring to the previous exercise, answer the following questions.

(a) How large a sample size n would be required to achieve a 99% confidence interval

estimate of p with a margin of error of 0.03?

(b) How large a sample size n would be required to achieve a 99% confidence interval

estimate of p with a margin of error of 0.025?