Statistics II Exam - 1st sitting – Duration: 120+30 minutes 统计考试代写 I. (2,5 points) In an opinion study, it is assumed that an unknown proportion of citizens – p – is in favour of a ne...View details
Exam – 2nd sitting
统计exam代写 Please be reminded to define all the relevant random variables and quantities and justify your answers carefully.
Please be reminded to define all the relevant random variables and quantities and justify your answers carefully.
Ø You are allowed to use a calculator.
Ø You are allowed to resort to printed documents and/or books.
Ø You are NOT allowed to write your answers with pencils or red ink. Only legible answers will be graded.
Ø You are NOT allowed to use any electronic device besides your calculator. Your exam will be annulled if this rule is violated.
Ø You are NOT allowed to leave the room during the first 30 minutes after the beginning of the exam, except in case of sudden indisposition. You are allowed to leave after 30 minutes after handing in your exam.
Ø The exam must be solved on the provided sheets, which must remain stapled.
The Quality Manager of a textile company is responsible for certifying that face masks are manufactured according to legal specifications. For this purpose, a data team recorded the number of times a face mask can be washed without affecting its performance. The data below reports the results of an analysis performed on a random sample of 150 masks:
(0,5) a) Compute the cumulative absolute frequencies.
(0,5) b) What is the percentage of masks that remained unaffected after 20 or more washes?
(1,0) c) Complete the following sentences, justifying your calculations:
i. “The number of times a mask can be washed without affecting its performance showed a variability around the mean of _____ washes.”
ii. “For ¾ of masks analysed, the performance remained unafected after _____ washes or less.”
iii. “A greater number of masks maintained its performance after _____ washes.”
(0,5) d) Evaluate the presence of outliers in the sample.
The daily demand for a certain type of dessert is a random variable with the following probability function:
(1,0) a) Calculate k.
(1,5) b) Assume that each unit of this dessert is sold for EUR 10. The manufacturer produces 3 units daily. Also, any dessert that remains unsold at the end of the day must be discarded at a loss of EUR 4. How much does the manufacturer expect to earn on a given day?
Student grades obtained in an exam follow a normal distribution, with mean 12 and standard deviation 2,38 points.
Exams were grouped into three categories:
1. Insufficient – Less than 10 points
2. Sufficient – Between 10 and 14 points
3. Good – More than 14 points
(1,5) a) If you select a group of 20 students at random, what is the probability of finding between 5 and 10 students (closed interval) whose exam has been classified as “Sufficient”?
(1,5) b) In a random sample of 100 students, what is the probability of observing at least 50 and at most 65 students whose exam has been classified as “Sufficient”?
The number of incoming calls at a call center, per minute, is known to follow the probability density function:
(1,0) a) Calculate the probability of, in a given minute, the number of incoming calls being at most 3.
(0,5) b) Calculate the variance of the variable of interest.
Comment on the logical value (TRUE or FALSE) of the following propositions, and explain your answer:
(1,0) a) T is unbiased for θ.
(1,0) b) T tends to underestimate θ.
Let S2 and S’2 be two estimators for the variance of normal population (σ2), such that:
(2,5) a) Show that both estimators are Mean Square Error consistent.
(1,0) b) Calculate their asymptotic relative efficiency and comment on the result.