IME 467 (Statistics) Test I

Summer 2015 

Name________________________

• You can either type in this problem sheet or write your answers on paper and scan it. Select the one that saves your time more.  Circle your answer in red if possible.
• Show all calculations except for problems 1 and 2. Without calculations, no points.
• This test is 80 min; 10 minutes are added to the test for down loading and up loading the files. 5 min late: 10% off.  10 min late: 20% off. No grading after that.  If you have complications when submitting your answers, use email right away and explain why you have to use email in detail.  If your reason makes sense I will consider no penalty for that.

1. (8 pts) True False questions.
1. (T, F) I am interested in the percentage of people who smoke in each state.  The data level of this data is “interval.”  
2. (T/ F) A study without researcher intervention is called a noninvolvement study.
3. (T, F)  When a person said the average salary is increased by 10%, the other person said only 40% of people had increased salary.  This is an example of detached statistics.
4. (T, F) The central limit theorem says the mean of a sample closely follows a Normal distribution when the sample size is large for any continuous and discrete population distributions.

1. (12 pts) Fill in the blanks.
1. In inferential statistics, we want to understand some characteristics of a (               ) using a sample.
2. Write a notation of a sample variance:    (               ).
3. We are rolling a die two times.  What is the sample space?  In this experiment, the order of outcome is not important.  S={                                                                                                                          }
4. I want to know how much time high school students are sleeping a day. I grouped all students by the grade: from grades 9 to 12. Furthermore, I divided each group of each grade into two: male and female groups.  In total I have 8 groups.  I selected four students from each of these 8 groups. What is the sampling technique is this? (                             )
5. I have five male students and four female students.  I select three at random out of these nine students.  I want to know the distribution of the number of female students selected.  What is the distribution of this value?  (Just give the name, or type of the distribution, e.g., uniform distribution)     (                             )
6. We are checking the effect of new way of doing a manual task. For that, we observe the workers and do time study.  At that time, realizing they are watched, the workers became more diligent in the job.  This is an example of (                  ) variable of an experimental study.  
2. (24 pts) Determine these statistics.
1. Mr. AA wants to calculate the mean waiting time of customers for service.  He found the waiting times are 4.3, 3.5 and 4.7 minutes for the three people observed.  Some of the customers are more important than the others.  So, he gave weights to them.  The weights are 1, 2, 3, respectively, in the order of the survey data shown above. Determine its weighted average of the customer waiting time.

1. I have this data: 1, 8, and 9.  Determine the variance of this sample.

1. I have this data: 5, 7, 12, 15, 20, 31, 32, 44, 45, 47, 51, 53, 55, 59, 60, 61, 67, and 69.  (Sample size: 18) What is the percentile of data value of 53?

1. (32 pts) Determine the probabilities
1. We roll a die 10 times.  What is the probability that we get the outcome of “1” three times from the ten trials?

1. A group of people are offered possible wonderful vacation packages to Hawaii.  It gives three tickets to us: one for a man and two for women.  There are 5 men and 10 women in my group.  When we select one man and two women, what is the probability that both I and my fiancé (all are in the group) are selected?

1. The weight of students in an engineering college follows a normal distribution, N(125, 20) (lb).  When we select a student, find the probability that the selected student has the weights less than 118 lb.

1. The weight of students in an engineering college follows a normal distribution, N(125, 20) (lb).  When we select five students, find the probability that the calculated sample mean of the weight is less than 118 lb

1. (24 pts) Other problems
1. I have two random variables, X and Y.  Their probability distributions are as follows. Determine this expected value: E[2X+Y].

1. I have this data {2, 4, 14, 15, 17, 22, 26, 28, 32, 35, 37, 39, 40, 41, 42, 43, 47, 50, 53, 56, 59, 60, 63, 64, 68, 69, 70, 71}  I want to make a frequency distribution table.  I want to use five classes.  Determine the lower class limit and lower class boundary of the third class.  Follow the procedure recommended by the textbook.

1. We have seven dogs. We select five of them, and line them up.  How many different line ups are possible?  (Order is important)