Norton University

NORTON UNIVERSITY

College of Social Science

Assignment A

Subject: Introduction to Statistics II

Lecturer: Mr. Mong Mara

1) Give the definition of a random variable.

2) List the main characteristics of Normal Random Variable.

3) What is a normal standard distribution?

4) Find the area under the standard normal distribution curve

a) Between and

b) Between and

c) Between

d) Between

e) To the right of

f) To the left of

g) Between

5) Find the probabilities for each using the standard normal distribution

6) Find the Z value to the right of the mean so that

a) 53.98% of the area under the distribution curve lies to the left of it.

b) 71.90% of the area under the distribution curve lies to the left of it.

c) 96.78% of the area under the distribution curve lies to the left of it.

7) An important quality characteristic for soft-drink bottlers is the amount of soft drink injected into each bottle. This volume is determined (approximately) by measuring the height of the soft drink in the neck of the bottle and comparing it to a scale that converts the height measurement to a volume measurement (Montgomery, 1985). In a particular filling process, the number of ounces injected into 8-ounce bottles is approximately normally distributed with mean 8.00 ounces and standard deviation 0.05 ounce. Bottles that contain less than 7.9 ounces do not meet the bottler’s quality standard and are sold at a substantial discount.

a) If 20000 bottles are filled, approximately how many will fail to meet the quality standard.

b) Suppose that, due to the failure of one of the filling system’s components, the mean of the filling process shifts to 7.95. (Assume that the standard deviation remain 0.05 ounce.) If 20000 bottles are filled, approximately how many will fail to meet the quality standard?

c) Suppose that a different component fails and, although the mean of the filling process remains 8.00 ounces, the standard deviation increases to 0.1 ounce. If 20000 bottles are filled, approximately how many will fail to meet the quality standard?

8) Dr. Moon has five students doing special independent study this semester. To evaluate their reading progress, Dr. Moon gave the students a five-question true/false test. The number of correct answers for each student is given below

Student / Number correct
Dara / 4
Vanna / 3
Nearyroth / 5
Sothun / 3
Rithy / 2

a) How many samples of 2 students are possible from this population?

b) List all possible samples of size 2, and compute the sample means.

c) Organize the sample means into a sampling distribution.

d) Compute the mean of the sample means, and compare it with the population mean.

e) Compare the shape of the population and the shape of the sampling distribution of the sample means.

9) In a poll to estimate residential popularity, each person in a random sample of 1000 were asked to agree with one of the following statements:

The president is doing a good job.
The president is doing a poor job
I have no opinion

A total of 560 respondents selected the first statement, indicating they thought the president was doing a good job.

a) Construct a 95 percent confidence interval for the proportion of respondents who feel the President is doing a good job.

b) Based on your interval in part (a), is it reasonable to conclude that a majority (more than half) of the population believe the president is doing a good job?

10) The mean number of travel days per year for outside salespeople is to be estimated. The 0.90 degree of confidence is to be used. The mean of a small pilot study was 150 days, with standard deviation of 14 days. If the population mean is to be estimated within 2 days, how many outside salespeople should be sampled?

11) A motorist claims that the Police in a city issue an average of 60 speeding tickets per day. These data show the number of speeding tickets issued each day for a period of one month. Assume. Is there enough evidence to reject the motorist’s claim at . Compute the p-value and interpret it.

12) A study is made comparing the cost to rent a one-bedroom apartment in Cincinnati with the corresponding cost of similar apartments in Pittsburgh. A sample of 35 apartments in Cincinnati showed the mean rental rate to be $370, with a standard deviation of $30. A sample of 40 apartments in Pittsburgh showed the mean rate to be $380, with a standard deviation of $26. At the 0.05 significance level is there a mean difference in mean rental rate between Cincinnati and Pittsburgh? (Use the five-step hypothesis-testing procedure.) Compute p-value and interpret it.

13) Research at the University of Toledo indicates that 50 percent of the students change their major area of study after their first year in a program. A random sample of 100 students in the college of business revealed that 48 had changed their major area of study after their first year of the program. Has there been a significance decrease of the proportion of students who change their major after the first year in this program? Test at 0.05 level of significance.

14) The Rope Organization conducted identical surveys in 1977 and 1997. One question asked women was “Are most men basically kind, gentle and thoughtful?” The 1977 survey revealed that of 3000 women surveyed, 2010 said that they were. In 1997, 1530 of 3000 women surveyed thought that men were kind, gentle and thoughtful. At the 0.05 level, can we conclude that women think men are less kind, gentle and thoughtful in 1997 compared with 1977?

15) Is there a difference in the proportion of college men and college women who smoke at least a pack of cigarettes a day at Northern State University? A sample of 400 women revealed 72 smoked at least one pack per day. A sample of 500 men revealed that 70 smoked at least one pack per day. At the 0.05 level of significance, is there a difference between the proportion of men and the proportion of women who smoke at least one pack of cigarettes a day, or can the difference in the proportions be attributed to sampling error?

16) Suppose the manufacturer of Advil developed a new formulation of the drug that is claimed to be more effective in relieving a headache than the one currently sold. To evaluate the new drug a sample of 200 current users is asked to try it. After one-month trial, 180 indicated the new drug was more effective in relieving a headache. At the same time a sample of 300 current Advil users is given the current drug but told it is the new formulation. From this group, 256 said it was an improvement. At the 0.05 significance level can we conclude that the new drug is more effective?

NORTON UNIVERSITY

College of Social Science

Assignment B

Subject: Introduction to Statistics II

Lecturer: Mr. Mong Mara

1) Give the definition of random variable.

2) List the main characteristics of Normal Random Variable.

3) What is a normal standard distribution?

4) Find the area under the standard normal distribution curve

a) Between

b) Between

c) To the left of

d) To the left of

e) To the right of

f) To the left of and to the right of

5) Find the probabilities for each using the standard normal distribution

6) Find the z value to the left of the mean so that

a) 98.87% of the area under the distribution curve lies to the right of it.

b) 82.12% of the area under the distribution curve lies to the right of it.

c) 60.64% of the area under the distribution curve lies to the right of it.

a) If 20000 bottles are filled, approximately how many will fail to meet the quality standard.

8) Professor Hann has six students doing special independent study this semester. To evaluate their reading progress, Dr. Hann gave the students a five-question true/false test. The number of correct answers for each student is given below

Student / Number correct
Dara / 3
Vanna / 4
Nearyroth / 5
Sothun / 3
Rithy / 2
Thoeun / 4

a) How many samples of 2 students are possible from this population?

b) List all possible samples of size 2, and compute the sample means.

c) Organize the sample means into a sampling distribution.

d) Compute the mean of the sample means, and compare it with the population mean.

e) Compare the shape of the population and the shape of the sampling distribution of the sample means.

9) The Human Relations Department of Electronics, In. would like to include a dental plan as part of the benefits package. The question is: How much does a typical employee and their family spend per year on dental expenses? A sample of 45 employees showed the mean amount spent last year was $1,820, with a standard deviation of $660.

a) Construct a 95 percent confidence interval for the population mean

b) The information in part (a) was given to the president of Electronics, Inc. He indicated he could afford $1,700 of employee dental expenses per year. Is it possible that the population mean could be $1700? Justify your answer.

10) The proportion of public accountants who had changed companies within three years is to be estimated within 3 percent. The 0.95 degree of confidence is to be used. A study conducted several years ago revealed that the percent of public accountants changing companies within three years was 21.

a) To update this study, the files of how many public accountants should be studied.

b) How many public accountants would be contacted if no previous estimates were available?

11) A coffee manufacturer is interested in finding out whether the men daily consumption of regular-coffee drinkers is less than that of decaffeinated-coffee drinkers. A random sample of 50 regular-coffee drinkers showed a mean of 4.35 cups per day, with a standard deviation of 1.20 cups per day. A sample of 40 decaffeinated-coffee drinkers showed a mean of 5.84 cups per day, with a standard deviation of 1.36 cups per day. Use the 0.01 significance level. Compute the p-value.

15) Damon family owns a large vineyard in western New York. The grapevines must be sprayed at the beginning of the growing season to protect against various insects and diseases. Two new insecticides have just been marketed: Pernod 5 and Action. To test their effectiveness, three long rows were selected and sprayed with Pernod 5 and three other were sprayed with Action. When the grapes ripened, 400 of the vines treated with Pernod 5 were checked for infestation. Likewise, a sample of 400 vines sprayed with Action was checked. The result are

insecticide / Number of vines checked / Number of infested vines
Pernod 5 / 400 / 24
Action / 400 / 40