I need help with my statistics exam. It include poisson probability distribution, time series analysis, anova, excel, descriptive statistics, normal distribution, binomial probability,?
TEACHER:_____________________________ 2014/2015 Academic Year
Fall session EAI Program
Statistics for Business
COURSE INSTRUCTORS: Pierre Aboussouan
COURSE COORDINATOR: Audrey Dalmasso Ex 1 /6 Ex 2 /5 Ex 3 /17 Ex 4 /5 Ex 5 /4 Ex 6 /8 Ex 7 /13 Ex 8 /8 Ex 9 /8 Ex 10 /10 Ex 11 /12 Ex 12 /9 Result FINAL EXAM
Extrait du R?glement Int?rieur du SKEMA Business School
Chapitre VI - Fraude
Article 20 : Durant toute ?preuve ?crite, les ?tudiants devront s'abstenir de quitter la salle d'examen, sauf cas grave.
Article 21 : Les communications entre ?tudiants lors des examens sont interdites.
Article 23 :
23.1 - La simple possession d'un document non autoris? constat?e au cours d'une ?preuve ?crite ou l'utilisation de papier autre que
celui distribu? pour l'?preuve d'examen sera consid?r?e comme une tentative de fraude.
23.3 - Toute fraude caract?ris?e entra?nera l'exclusion imm?diate de l'?tudiant de la salle d'examen.
Article 24 : Tout ?tudiant ayant commis une fraude ou une tentative de fraude d?ment constat?e pourra ?tre traduit en Conseil de
Discipline, lequel a comp?tence pour prendre toute d?cision d'exclusion temporaire ou d?finitive de l'Ecole.
Lu et approuv?
Signature de l??tudiant : ??????????????.. -=-=-=-=-=-=-=-=-=Academic Regulations of SKEMA Business School
Chapter VI - Cheating
Article 20 : During exams, students are not allowed to exit the room, except in case of emergency.
Article 21 : It is strictly prohibited to communicate with any other student during the exam.
Article 23 :
23.1 - It is strictly prohibited during exams to possess any document or to use material or paper which has not been expressly
23.3 - Any student found in breach of these rules will be immediately expelled from the exam room.
Article 24 : Any student found guilty of cheating or trying to cheat will be presented to the Academic Committee whose sanction may
be as high as exclusion of the school.
Read and Approved
Student?s signature : ??????????????.. DIRECTIONS: Please, write clearly. The use of a pencil (crayon ? papier) is highly recommended. Answer on this exam paper and inside the dedicated areas. Please, do not unstaple pages.
If those first three conditions are not fulfilled, at least 4 points could be removed. Drafts or other paper sheets will not be graded. Les feuilles de brouillon ou autres ne seront pas not?es. A correct answer with no explanation may not get full credit but a wrong answer with intermediate
steps (method or calculation) may get partial credit. The use of non-programmable calculators is allowed. Students are not permitted to share a calculator.
105 points possible Exercise 1. Poisson Probability Distribution (6 points) During the peak fishing months, a marina at a large man-made reservoir noted that boats were arriving at the
average of 2.8 boats every 30 minutes to use the boat ramp. Let x be the number of boats arriving during the
next 30 minutes.
Direction: Round up to 4 digits after the decimal point.
1) What is the probability that during the next hour the number of boats arriving to load or unload is at most
two? Use the Poisson formula. 2) What is the probability that during the next 30 minutes the number of boats arriving to load or unload is
greater than one? Use the Poisson formula. 2 Exercise 2. Time Series Analysis (5 points) Here are data on the monthly price of gas, which is a component of the Consumer Price Index (CPI).
The CPI represents changes in prices of all goods and services purchased for consumption by urban
The data table shows the first months of year 2006.
3.033 5-month moving average 1. Compute a 5-month moving average of the first months of 2006. Fill in the previous table. Round to 3
digits after the decimal point.
Show your computation for the first value. 2. Use it to predict the value for September 2006. Justify. 3 Exercise 3. ANOVA (17 points) Spam is the price we pay to easily communicate using e-mail. Does spam affect everyone equally? In a
preliminary study, university professors, administrators, and students were randomly sampled. Each
person was asked to count the number of spam messages received that day. The results follow. Can we
infer at the 1% significance level that the differing university communities differ in the amount of spam
they receive in their e-mails?
Direction: Round up to 2 digits after the decimal point.
1. Determine the null hypothesis and H1. 2. The following tables are Excel screenshots but information are missing. Complete the cells shaded in
grey of the following tables. Explain your computations below.
Round to 3 digits after the decimal point when it is necessary.
Anova: Single Factor
Professor and Students
Source of Variation
6 SS Sum
42 df Average
10,5 MS Variance
21,667 F F crit 305
334,4 9 4 Do you reject H0? State why or why not. 4. Interpret this result. Does spam affect everyone equally? 5. James F. wants to verify those results and enter those parameters in the Anova Excel applet: Do you think that the procedure chosen by James is correct? If not, state why. Exercise 4. Descriptive Statistics (5 points)
5 The data represent the salaries (in thousands of dollars) of a sample of 14 employees of a firm:
40.01 29.6 28.2 27.2 26.5 24.8 24.3 23.7 23.5 22.7 21.1 20.4 20.2 11.9
a. Calculate the median salary. b. Compute the 28.572% trimmed mean. Exercise 5. Normal Distribution (4 points) The amount of time spent by American adults playing sports per week is normally distributed with a mean
of 5 hours and standard deviation of 1.25 hours. Find the probability that a randomly selected American
adult plays sport between 2 and 6.2 hours per week. Justify. 6 Exercise 6. Binomial Probabilities (8 points) A state senator believes that p = 70% of all senators on the Finance Committee will strongly support the tax
proposal she wishes to advance. X is the number of senators who strongly support the proposal and X is a
Round up to three digits after the decimal point. Justify.
1. Suppose that this belief is correct and that 5 senators are approached at random. Calculate the following
probabilities, using either the binomial formula or the binomial cumulative table (Appendix 2).
a) What is the probability that more than three of the 5 will strongly support the proposal? b) What is the probability exactly 2 senators will strongly support the proposal? 2. Suppose that this belief is correct and that 9 senators are approached at random. What is the probability
that at least 4 of the 9 will strongly support the proposal?
Use the binomial distribution table (Appendix 3). 7 Exercise 7. Descriptive Statistics and Hypothesis Testing (13 points) Is your favorite TV program often interrupted by advertising? CNBC presented statistics on the average
number of programming minutes in a half-hour sitcom. The following data (in minutes) are representative
of its finding:
Assume the population is approximately normal.
1. a) Calculate the sample mean (round up to 2 digits after the decimal point), b) Compute the interquartile range. Show all the steps. 2. Prove that the sample variance is 1.74 minutes and the sample standard deviation is 1.32.
23.82 8 3. CNBC claims that the population average number programming minutes (?) in a half-hour sitcom
is more than 21.93 minutes (H1). The sample standard deviation is 1.32 and the value of ? is the
one found in question 1. The sample size is still 7.
a) Determine H0. Is it a one-tail test or a two-tail test? b) Does the sample evidence contradict this claim at = 10%? Exercise 8. Hypothesis Testing (8 points) An experimenter is interested on the hypothesis testing problem:
H0 : ? = 420 versus H1: ? ? 420
where ? is the average radiation level in a research laboratory. Suppose that a sample of n = 29 radiation
level measurement is obtained and the experimenter wishes to use a value of the population variance is 100
for the population of the radiation levels. Suppose the sample mean is 415.7.
1) Is it a one-tail or a two-tail-test? 2) Does the experimenter accept the null hypothesis with a significance level = 5%? 9 3) Check you result by computing the P-value. Compare with alpha and conclude. Exercise 9. Confidence interval of the population mean (8 points) A cost accountant wishes to establish the average amount, ?, spent by executives per day on travel and
lodging. Then a comparison, between the average and the amount turned in to be reimbursed, will be made
and unreasonably high or low expense amounts audited.
A random sample of 50 executive expense receipts is taken. The average in the sample was $208. From a
similar survey the population standard deviation of the amounts is approximately $29.
The accountant prepares a 90-percent confidence level for ?. What is the confidence interval?
Direction: Round up to 3 digits after the decimal point. 10 Exercise 10. Probabilities (10 points) A survey of 1000 randomly selected married women showed that 660 of these women have one or more
children (Event A), while the rest have no children (Event ?).
Out of these 1000 women, 360 are working women (Event B)
( ? ) = 0.25
A woman is randomly selected.
Direction: Round up to 2 digits after the decimal point.
1) Fill in the following contingency table with probabilities. Justify your computations. ? ? 2) What is the probability that this woman is a working?woman given that she has one or more
children? 3) What is the probability that she is either a working?woman or has no children? 4) Are the events ?working?woman? and ?has one or more children? independent? Why or why not? 11 Exercise 11. Measures of association (12 points) Table below lists the weight (in pounds) and length (in inches) for 11 largemouth bass (Source: The
Mathematics Teacher, 1997, p. 666). Let those observations be population data.
Note that in this table, the coma "," means "." the decimal dot.
Table 1. Excel screenshot 1) Using the previous data, compute the population covariance. Interpret it. 2) a. Using the previous data, find a simple linear regression model for predicting the weight of a
largemouth bass from knowledge of its length. b. If the length of a largemouth bass caught is 15.00 inches. What is the expected weight?
12 3) Using Excel command in English, indicate what we need to type up to compute the population
variance of X. Be precise. 4) The coefficient of determination is 94.67%. Do you see any problems in using linear relationship as a
model for these data? Justify. Exercise 12. Normal distribution and beta (9 points) Suppose the null hypothesis H0 is that the population mean is greater than or equal to 340.
Suppose further that a random sample of 41 items is taken and the population standard deviation is 25. = 0.10
1. What is the alternative hypothesis? 2. Compute the probability of committing a Type II error if the population mean is actually 341.
a) Stage 1 (Round the final result to 3 digits after the decimal point). b) Stage 2. Compute . 13 3. What happens to the value of as n gets smaller? (Note: Do not calculate the new beta .) 14
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