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Statistics II: Problem Sets 1 and 2

统计作业代写 Dear Students, Given the current state of affairs, in which we are facing a worldwide pandemic, the traditional methods of evaluation and


Dear Students,

Given the current state of affairs, in which we are facing a worldwide pandemic, the traditional methods of evaluation and teaching have been adapted accordingly.

The Statistics II course is not an exception. From my part, I would like to take the opportunity to extend you a word of appreciation for the cooperation of the last weeks.

With respect to the problem sets, a few notes:

1.Google Form link:

2.The goal is not only to evaluate but also to promote a continuous study of the course materials;

3.The 5 (five) problem sets split the course topics in segments, to help you organiseand ease your study;

4.The problem sets:

(a) May be solved in groups of up to 3 (three) students (same class only);

(b) Must be solved by hand, clearly and concisely (two exercises per page). Illegible documents will not be graded;

(c) Must be identified (name(s), number(s) and class);

5.The third group in this problem set (3 Extra Mile) is optional and not for the faint of heart.

1 Confidence Intervals 统计作业代写

Confidence, S.A. is a company dedicated to the production and promotion of music and concerts in Portugal.

Its activity consists in brokering venues, renting out hardware and hiring of expert personnel. It also functions as an artist agency.

Joseph Toolo, director and sole shareholder of Confidence, S.A. is planning the company’s activities for 2021 – particularly relevant due to the several cancellations which took place in 2020 and led to a significant revenue decline – and, to help enlighten some of his decisions, he decided to hire Joanne Medianne, a Quantitative Methods specialist.

In order to confirm her results, Mrs. Medianne asked you to do some double-checks (in exchange for concert tickets). Based on the information presented below, help Mrs. Medianne as best as you can:

Mr. Toolo is planning two concerts of a famous artist, ´Eric Clepto, one in Lisbon and one in Porto. Unfortunately, due to Mr. Clepto’s busy schedule, only one of the concerts can take place, at Mr. Toolo’s choice.

To solve this problem, Mrs. Medianne proposed conducting two surveys, one in each city, in order to quantify the proportion of fans of ´Eric Clepto. The results are presented below:

No. surveyed10001000


Based on a confidence interval for the difference in proportions (λ = 0, 95), Mrs. Medianne plans on proposing that Mr. Toolo chooses Porto for the concert. Do you corroborate Mrs. Medianne’s recommendation? Why? 统计作业代写


To perform a sensitivity analysis, Mrs. Medianne asked you to construct a new confidence interval (λ = 0, 96) based on the previous one. If the sample proportions remain constant, what sample size obtained in Porto (n2) would lead Mr. Toolo to choose Lisbon for the concert if the sample obtained therein consisted of 2000 respondents (n1= 2000)?


Mrs. Medianne will submit a document to Mr. Toolo containing her conclusions and recommendations. An excerpt of this document is presented below:

Taking into account the calculated confidence interval, we conclude that the probability of the true difference in proportions lying between those two specific bounds is 0,95.

Is Mrs. Medianne conveying correct information to Mr. Toolo? Explain.

2 Parametric Hypothesis Tests 统计作业代写

Una Volta Ogni Tanto (UVOT), SpA is the current holder of a state passenger railway contract in a certain municipality of southern Italy.

There are two railway lines in the municipality: the Red line and the Yellow line.

The contract expires in December 2020, and the competent state authority will audit the company’s service levels in order to assess if the contract should be renewed until 2040. To that effect, the state hired Jonathan Askew, a Quantitative Methods specialist, to shed some light on the questions at hand.

Below you will find the problems Jonathan is facing. Answer the following questions in order to validate his results:


One of the contract clauses stipulates that the average stoppage time at the stations, for both lines, should not exceed 30 (thirty) seconds. To check if the rule was being complied with, two samples were obtained (results below):


Resorting to hypotheses tests, what should Mr. Askew recommend (α = 0, 1)? Does he need to make any assumption to perform the tests? [define the populations, choose the appropriate test statistic, etc., and show your calculations]


Is Mr. Askew right? Consider the output (SPSS) below.

Verify all the values shown, indicating if they are consistent with your previous calculations for the Yellow Line. If you find inconsistent values, provide the correct number.


(b) Considering the decision made in (a), what type of Error may you be committing?

(c) Calculate the test’s statistical power at π(41) and π(121). Given that 41 and 121 are symmetrical around σ2 = 81, how do you explain the difference between the calculated values?

(d) Sketch the Power function, indicating its minimum value and the values calculated in (c).

3 Extra Mile 统计作业代写

Provide an explanation for the following fact:

For a two-sided hypothesis test, rejecting the null hypothesis necessarily

implies that the value established under H0 does not belong to theassociated confidence interval.


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