Write your name and number on ALL THE PAGES. No questions during the exam.Write with a pen. No pencils or red ink.
A sample of 400 households in City A revealed that 8% of homes were rental properties, whereas in City B a sample of 270 households contained 37 such homes.
a) [1 point] Calculate the 99% confidence interval for the percentage of non-rental properties in City B.
b) [1,5 point] Can you claim, statistically, that the percentage of rental properties is equal between City A and City B? Justify.
One of the major tasks of health institutions is the management, monitoring and prevention of smoking.
To those effects, surveys are conducted periodically. One survey concluded that, on average, Europeans (smokers and regular ex-smokers) started smoking at age 17,6 years. Several measures have been implemented to accomplish a continuous increase of the average age of smoking initiation. The current goal is set at 18 years.
Another (more recent) survey was conducted and some of the results are presented below:
Answer the following questions in context, i.e. given the available information. Mention any limitations and goals of the analysis.
a) [2 points] What is the specific purpose of each t test displayed above? Write the their null hypotheses. Justify and refer to respective output table.
b) [1,5 points] What can you conclude from the test in Table 1? Justify. Use a = 0,05.
c) [1 point] Calculate an approximate value for A and B. Justify your calculations.
d) [2,5 points] Are all assumptions verified for the t test in Table 3? If so, what can you conclude? Use a = 0,05.
e) [1 point] Comment on the following statement: There is no relationship betweenthe age of smoking initiation and gender.
An automaker is planning to launch four new models (M1, M2, M3 and M4) in four different countries (C1, C2, C3, C4). Before launching, the company wants to know if consumer preferences (for the new models) are influenced by the country of residence. To that end, the automaker will collect a random sample in each of the four countries and ask each respondent about their preferred model.
a) [0.5 points] Define the variables of interest and refer to their measurement scale.
b) [1 point] Indicate an appropriate test for this problem. Justify your answer and write the respective test statistic.
c) [1 point] Define the competing hypotheses and give recommendations for all possible outcomes.
d) [0.5 points] Indicate the assumptions required for this hypothesis test.
Answer the following questions clearly and concisely:
a) [0,75 points] Why are independence and goodness-of-fit Chi-Square tests right-tailed?
b) [0,75 points] Why are these tests called ‘non-parametric’?
c) [1 point] How should one proceed when rejecting the null hypothesis from ANOVA?
A company wants to model the sales of product W as a function of two independent variables: Product Price and Size of Sales Force. Based on sample of 16 periods, the following results were obtained:
a) [0,5 points] Write the equation of the estimated model.
b) [1,5 point] Interpret the standardized and unstandardized coefficients for the independent variable with greatest impact on the dependent variable.
c) [1 point] Calculate and interpret the coefficient of determination.
d) [1 point] In face of the results, would you suggest any change to the model? Justify.
