统计考试代做 Statistics代写 marginal probability functions代写
51统计考试代做 1. In a given community, the monthly savings of an individual follow a Normal distribution with mean 150 m.u. and standard deviation 4...
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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 new law being introduced,
Note: No questions during the exam! You are allowed to use your formula sheet, statistical tables and calculator.
In an opinion study, it is assumed that an unknown proportion of citizens – p – is in favour of a new law being introduced, and the remaining proportion – (1-p) – is against it. Researchers intend to collect a simple random sample of size n in order to study the public’s opinion. The sample proportion of citizens that is in favour of this new law will be used to estimate the true proportion p.
(1,5) a) What should be the sample size if we want a 95% confidence interval estimate to have a maximum error of 2%? Explain.
(1,0) b) Assume that a sample of 2400 citizens was collected. When surveyed about their opinion about the new law, 4,8% of citizens responded favourably. Calculate a 95% confidence interval for the true proportion of citizens in favour of the new law. Interpret the result.
An opinion study was conducted in order to evaluate which features are most valued regarding beer consumption. The relevance attributed to brand, one of the features, was analysed. The analysis produced the results below (Note: the variable was measured on a scale from 1 – Very Relevant to 10 – Not Relevant):
(0,5) a) State the hypotheses being tested above.
(1,5) b) What decision should be made (α=0,05)? What can you conclude?
(1,0) c) Use the output data to test the hypothesis H1: µ=3. What decision should be made (α=0,05)?
The management team of a media company wants to analyse reader behaviour, namely the average reading time (in minutes) of a particular newspaper. The average reading time is currently known to be at least 90 minutes. Also, it is reasonable to assume that the average reading time (in minutes) follows a normal distribution with variance 225 minutes^{2}.
Due to budget and time constraints, a sample of only 16 readers was collected. The significance level for hypothesis testing is set at 0,05.
(1,50) a) What is the probability of rejecting the current belief about reading habits, if the true average reading time is in fact 80 minutes?
(1,00) a) Recalculate the probability of the previous question if the media company is able to collect a sample of size 64. Comment.
An opinion study was conducted regarding the occurrence of the Eurovision Festival in Portugal. Based on a phone book record, 218 individuals were sampled at random.
Taking into account the individual assessment of the festival’s occurence (1: very bad to 5: very good), according to gender, the following results were obtained:
a) Which statistical test is being applied above? Write the hypotheses being tested.
b) Calculate the values a and b, missing from the table.
c) Make a decision (explain the entire decision process), within the problem’s context (α= 0,05).
In order to estimate the economic impact of the Eurovision Festival, a research team attempted to relate formal education level (high, mid, low) and the economic relevance attributed to this event (measured on a scale from 0 – irrelevant to 10 – very relevant). The following results were found:
a) What is intended with this analysis? Write the hypotheses that underlie the ANOVA table.
b) Which are the assumptions underlying the model? Do you have elements for verification? What can you conclude?
c) Taking into account the formal education level, what can you conclude about the economic relevance attributed to the Festival? Present a thorough conclusion, including a statistical decision and taking into account all available information (α= 0,05).
A logistics company wants to construct a model to explain sales of product A as a function of the following independent variables: Price of product A and Bonus paid to salesforce of product A. Based on a sample of the most recent fiscal years, a model was estimated, having produced the following results:
a) Does the model provide a good fit to the data? Write the hypothesis being tested and decide accordingly.
b) Write the equation for the estimated model.
c) Based on the estimated model, interpret the unstandardised coefficient calculated for the variable Price of Product A (m.u.).
d) For α = 0,05, should you be inclined to believe that both independent variables are good predictors of the dependent variable? Write the hypotheses on which you are basing your decision as well as the respective test results.
e) Calculate the coefficient of determination. Comment.
An automaker is launching a new car model. In the process, it selected as target group the owners of Renault, Fiat and Citroen cars acquired last year.
To collect information about consumer satisfaction within the target population, the automaker hired a data analytics company to collect a random sample of 100 such consumers.
The sample data showed the following distribution: 50 Renault, 25 Fiat and 25 Citroen. Nevertheless, available data from a state entity shows that last year sales were distributed as follows: 70% Renault, 20% Fiat and 10% Citroen. For a significance level of 5%, should you assume that the sample was in fact randomly obtained by the analytics company?
This question is made up of 6 multiple choice questions. Mark your answer by filling the corresponding square. A correct answer is worth 0,5 points. An incorrect answer is worth negative 0,15 points. You do not need to justify your choice. 12 minutes should suffice to complete the 6 questions.
Within the scope of statistical decision making, results are said to be significant based on:
□ a) the p-value
□ b) the null hypothesis
□ c) the test value
□ d) the alternative hypothesis
When performing a simple, parametric analysis of variance, if the calculated test statistic, F, exceeds the critical value, which decision should be made?
□ a) Reject H0, as there is evidence supporting that all group means are different
□ b) Not reject H0 due to miscalculation
□ c) Reject H0, as there is evidence supporting that one or more group means are different from the remaining
□ d) Not reject H0, as there is no evidence supportive of group mean differences
In a simple, parametric analysis of variance, the number of degrees of freedom associated with SSB is:
□ a) the number of groups
□ b) the number of observations minus 1
□ c) the number of observations minus the number of groups
□ d) the number of groups minus 1
The null hypothesis of an Independence Chi-Square test states that:
□ a) there is a relationship between two categorical variables
□ b) there is a relationship between two metric variables
□ c) there is not a relationship between two categorical variables
□ d) there is not a relationship between two metric variables
Which of the following conditions occurs when multicollinearity is found on a multiple linear regression model?
□ a) the residuals are correlated
□ b) the data is a time series
□ c) the independent variables are correlated
□ d) residuals are not constant for all estimated values of Y
Numa análise de variância simples paramétrica, com três grupos, se H_{0},é rejeitada, qual das seguintes afirmações é verdadeira? When performing a simple, parametric analysis of variance, with 3 groups, if H0 is
rejected, which of the following statements is true?
□ a) the group means are all different
□ b) three of the groups have different means
□ c) at least one pair of means is different
□ d) group variances are different
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