¡Descarga examen junio 2016 ingles y más Exámenes en PDF de Estadística Empresarial solo en Docsity!
URJC – GADE BILINGÜE - CORPORATE STATISTICS II
June 2016 Exam
(model X)
EXAM DURATION: 100 MINUTES
The exam has two sections:
Section A: Multiple Choice (pages 2-4) with 10 questions, weighting 40% of the final grade.
ONLY THOSE ANSWERS MARKED IN THE MASK WILL BE CONSIDERED. At the end of
this section there is space to carry out calculations if needed.
A correct answer adds 1 point. A wrong answer subtracts 0.2 points. A question not answered
adds 0 points. A minimum grade of 4 points in this section is required for assessing
section B and for passing the exam.
Section B: Problem Solving (pages 5-12) with 4 exercises weighting 60% of the total grade.
A minimum grade of 5 points in this section is required to pass.
The final grade will be the result of adding 40% of section A and 60% of section B. A minimum
final grade of 5 points is required to pass.
MULTIPLE CHOICE ANSWERS
A
X X
B
X
C
X X X
D
X X X X
SURNAMES: NAME
DNI:
Group:
B:PROBLEM
SOLVING
(60% weight) POINTS STUDENT
A: MULTIPLE CHOICE (40% weight)
Exercise 1 2
Exercise 2
2
RIGHT (+ 1/10)
Exercise 3
4
WRONG (-0.2/10) - Exercise 4 2
MC GRADE out of 10 PS GRADE out of 10
40 % 60%
FINAL
GRADE
SECTION A: TEST
1.- Choose the right answer regarding a hypothesis testing in which the null hypothesis is rejected with
α = 5% but accepted with α = 1%:
a) The p-value is higher than 1% but lower than 5%
b) The p-value is higher than 5%
c) The p-value is lower than 1%
d) The situation formulated in the statement can never take place
2.- Suppose we want to compare the population variances of two normal variables
௫
௫
௬
௬
൯. Then we take two independent s.r.s. of a given size, one from each
variable, and obtain a 95% confidence interval estimate for the quotient of variances with this result:
௫
ଶ
௬
ଶ
ఊୀ,ଽହ
Choose the right answer at that level of confidence:
a) ߪ ௫
ଶ
௬
ଶ
b) ߪ ௫
ଶ
௬
ଶ
c) ߪ ௫
ଶ
௬
ଶ
d) We can only get conclusions when we use a 100% level of confidence interval estimate
3.- Choose the right answer regarding the sampling distribution of a point estimator:
a) This means that the point estimator is an unbiased estimator
b) This means that the point estimator is an efficient estimator
c) This means that the point estimator is a consistent estimator
d) This means that the point estimator is a random variable
4.- Choose the right answer regarding a hypothesis test consisting in comparing the observed (absolute)
frequencies in the sample with those expected under the theoretical distribution being tested:
a) It is the goodness of fit Kolmogorov-Smirnov test
b) It is the goodness of fit Shapiro-Wilks test
c) It is a parametric test for the mean in a normal variable
d) It is the goodness of fit Pearson’s Chi square test
5.- Which one is the maximum likelihood (ML) point estimator of the population proportion in a B(1;p)
once a s.r.s. of size n has been obtained?
a) The first element in the sample ݔ ଵ
b) The last element in the sample ݔ
c) The inverse of the sample mean
ଵ
௫̅
d) The sample mean ݔ̅
6.- Which of the following features correspond to a simple random sample?
a) Each element in the population have the same probability to be included in the sample
b) Each element in the sample is independent in probability from other ones when replacement is considered
c) Each element in the sample has the same probability distribution than the variable under study
d) The three previous statements are true
PROBLEM SOLVING SECTION
Exercise 1 (2 points)
A pharmaceutical company has launched a new medicine for certain disease. The company assures that
patients recover in less than 5 days. In order to test this hypothesis a group of doctors have applied this
medicine to a s.r.s. of 20 patients in a given hospital. Data concerning the recovery time measured in days
(variable X) obtained from the sample has been:
ଶ
Assuming that X follows a N(μ x
;σ), answer:
a) Elaborate the corresponding test under the point of view of the pharmaceutical company with α = 1%,
formulating the hypothesis, the test statistic, the critical region and the decision made. Also solve using
the p-value. (1,5 points)
b) Discuss the kind of error which could be incurred arising from the decision made and the associated
probability. (0,5 points)
Exercise 2 (2 points)
In the context of the previous exercise, the group of doctors want to compare the effectiveness of the new
medicine to that achieved with the medicine they were using so far. Calling Y the variable consisting in the
recovery time measured in days for those patients being treated with the old medicine, the doctors have
collected the following data from Y based on a s.r.s. of 20 different patients:
ଶ
Assuming that Y follows a N(μ y
;σ), both samples are independent and both variables X and Y have the
same unknown standard deviation σ, answer:
a) Run a test to check if there are significative differences between the population means μ x
and μ y
at a
1% level of significance, formulating the hypothesis, the test statistic, the critical region and the
decision made. Also solve using the p-value. (1,5 points)
b) Discuss the kind of error which could be incurred arising from the decision made and the associated
probability. (0,5 points)
Exercise 4 (2 points)
Finally, the group of doctors want to know if the appearance of adverse reactions does not depend on the
age of the patient. For this purpose they have considered three age stratus: 18-45; 46-70; beyond 70.
Therefore supported by the s.r.s. of the previous exercise the distribution of patients by age has been:
18-45 46-70 beyond 70
Patient having adverse reactions 4 4 8
Patient not having adverse reactions 29 31 24
Run an independence test at a 5 % significance level, formulating the hypothesis, the test statistic, the
critical region and the decision made. Also solve using the p-value.
