Consider all random samples of 100 test scores. What is the standard deviation

1.True or False. Justify for full credit.

.                             (a)  A is an event, and Ac is the complement of A, then P(A AND Ac ) = 0. 


.                             (b)  If the variance of a data set is 0, then all the observations in this data set must be zero. 


.                             (c)  If a 95% confidence interval for a population mean contains 1, then the 90% confidence 
interval for the same parameter must contain 1 


.                             (d)  When plotted on the same graph, a distribution with a mean of 40 and a standard deviation 
of 10 will look more spread out than a distribution with a mean of 50 and standard 
deviation of 5. 


.                             (e)  In a two-tailed test, the value of a test statistic is 2. The test statistic follows a distribution 
with the distribution curve shown below. If we know the shaded area is 0.03, then we have sufficient evidence to reject the null hypothesis at 0.05 level of significance. 


2.Choose the best answer. Justify for full credit. 


(a) A study was conducted at a local college to analyze the average GPA of students graduated from UMUC in 2015. 100 students graduated from UMUC in 2015 were randomly selected,

1.                 

and (i)

(ii) (iii)

(b) The (i)

(ii) (iii) (iv)

the average GPA for the group is 3.5. The value 3.5 is a statistic

parameter
cannot be determined

hotel ratings are usually on a scale from 0 star to 5 stars. The level of this measurement is interval

nominal ordinal ratio

(c) On the Election Day, UMUC News Club organized an exit poll in which specific polling stations were randomly selected and all voters were surveyed as they left those polling stations. This type of sampling is called:

(i) cluster

STAT 200: Introduction to Statistics Final Examination, Fall 2016 OL4 Page 3 of 8

.      (ii)  convenience 


.      (iii)  systematic 


.      (iv)  stratified 


3. Choose the best answer. Justify for full credit.

.      (a)  A study of 10 different weight loss programs involved 500 subjects. Each of the 10 programs had 50 subjects in it. The subjects were followed for 12 months. Weight change for each subject was recorded. You want to test the claim that the mean weight loss is the same for the 10 programs. What statistical approach should be used?

.                              (i)  t-test 


.                              (ii)  linear regression 


.                              (iii)  ANOV A 


.                              (iv)  confidence interval 


.      (b)  A STAT 200 instructor teaches two classes. She wants to test if the variances of the score distribution for the two classes are different. What type of hypothesis test should she use?

.                              (i)  t-test for two independent samples 


.                              (ii)  t-test for matched samples 


.                              (iii)  z-test for two samples 


.                              (iv)  F- test 


4. A random sample of 100 students was chosen from UMUC STAT 200 classes. The frequency distribution below shows the distribution for study time each week (in hours). (Show all work. Just the answer, without supporting work, will receive no credit.)

Study Time (in hours)

Frequency

Relative Frequency

0.0 – 4.9

5

5.0 - 9.9

13

10.0 - 14.9

0.22

15.0 -19.9

42

20.0 – 24.9

Total

100

.      (a)  Complete the frequency table with frequency and relative frequency. Express the relative frequency to three decimal places. 


.      (b)  What percentage of the study times was at least 15 hours? 


.      (c)  Does this distribution have positive skew or negative skew? Why or why not? 


STAT 200: Introduction to Statistics Final Examination, Fall 2016 OL4 Page 4 of 8

5. The five-number summary below shows the grade distribution of a STAT 200 quiz for a sample of 1000 students.

Answer each question based on the given information, and explain your answer in each case.

.      (a)  What is the interquartile range in the grade distribution? 


.      (b)  Which score band has the fewest students? 
(i) 20-60
(ii) 60 - 75
(iii) 75 - 90
(iv) Cannot be determined 


.      (c)  How many students are in the score band between 75 and 100? 


6. Consider selecting one card at a time from a 52-card deck. What is the probability that the first card is from the suit of hearts and the second card is also from the suit of hearts? (Note: There are 13 cards from the suit of hearts in a deck of cards) (Show all work. Just the answer, without supporting work, will receive no credit.)

.      (a)  Assuming the card selection is without replacement. 


.      (b)  Assuming the card selection is with replacement. 


7. There are 1000 students in a high school. Among the 1000 students, 150 students take AP Statistics, and 300 students take AP French. 100 students take both AP courses. Let S be the event that a randomly selected student takes AP Statistics, and F be the event that a randomly selected student takes AP French. Show all work. Just the answer, without supporting work, will receive no credit.

.      (a)  Provide a written description of the complement event of (S OR F). 


.      (b)  What is the probability of complement event of (S OR F)? 


STAT 200: Introduction to Statistics Final Examination, Fall 2016 OL4 Page 5 of 8

8. Consider rolling a fair 6-faced die twice. Let A be the event that the sum of the two rolls is at most 6, and B be the event that the first one is an even number.

.      (a)  What is the probability that the sum of the two rolls is at most 6 given that the first one is an even number? Show all work. Just the answer, without supporting work, will receive no credit. 


.      (b)  Are event A and event B independent? Explain. 


9. There are 6 books in the “Statistics is Fun” series. (Show all work. Just the answer, without supporting work, will receive no credit).

(a)  How many different ways can Mimi arrange the 6 books in her book shelf? 


(b)  "How many different ways can the THREE books be selected?"

.       

10.            Assume random variable x follows a probability distribution shown in the table below. Determine the mean and standard deviation of x. Show all work. Just the answer, without supporting work, will receive no credit. 


11.            Mimi joined UMUC basketball team since summer 2016. On average, she is able to score 30% of the field goals. Assume she tries 15 field goals in a game. 


.      (a)  Let X be the number of field goals that Mimi scores in the game. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively? 


.      (b)  Find the probability that Mimi scores at least 2 of the 15 field goals. (round the answer to 3 decimal places) Show all work. Just the answer, without supporting work, will receive no credit. 


12. A research concludes that the number of hours of exercise per week for adults is normally distributed with a mean of 3.5 hours and a standard deviation of 3 hours. Show all work. Just the answer, without supporting work, will receive no credit.

.      (a)  Find the 75th percentile for the distribution of exercise time per week. (round the answer to 2 decimal places) 


.      (b)  What is the probability that a randomly selected adult has more than 5 hours of exercise per week? (round the answer to 4 decimal places) 


13. Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 500 and a standard deviation of 100. Show all work. Just the answer, without supporting work, will receive no credit.

x

-2

-1

0

1

2

P(x)

0.1

0.4

0.1

0.1

0.3