STA-1103 Business Statistics

General instructions: for each of the following problems and questions, write your answers clearly in a text file.

For answers requiring justification, be concise: except where a maximum number of words or lines is indicated, no individual answer can be more than one full sentence.

Resource producing countries are often thought to face a specific set of political constraints that influence the social, economic, and political conditions that prevail in their society. One version of this “resource curse” investigates links between the importance of oil in the economy and the likelihood of armed conflict.

In one of these studies, researchers attempt to focus on the possibility of a direct link between the two variables: the hypothesis would be that the degree of dependence on oil revenues of an economy is correlated with the prevalence of conflict.

In order to test this hypothesis, the researchers use the following two variables on a sample of 50 countries:

• Oildependence, expressed as one of three possibilities:
  • low(oil production accounts for less than 5% of GDP)
  • medium(oil production accounts for more than 5% of GDP but less than 20%)
  • high(oil production accounts for 20% or more of GDP)
• prevalenceof armed conflict over the past five years:
  • low(25 or less battle-related deaths per year)
  • medium(over 25 but less than 1000 battle-related deaths per year)
  • high(1000 battle-related deaths or over per year)

The results are presented in the following table:

Chi-squared statistic = 9.50, p =0.04979

1. Isthere a correlation between the two variables? What do these results allow you to say about the hypothesis of the authors?
2. Canyou say anything about the strength of the relationship? Be 
3. Supposethat the results from the Chi-Squared test gave us the following instead:

Chi-Squared statistic = 9.43, p = 0.0512 Would these results lead you to change your answers in a) above?

A survey asks respondents to rank the importance they give to certain issues during an electoral campaign, including environmental issues, the economy and job creation, foreign relations, etc.

For each issue, the survey asks the following question: “what is the importance that this issue should get in the current campaign?” The possible answers range from 1 (not important at all) to 5 (extremely important).

The researchers conduct the survey on a randomly selected sample of 100 people from the Ottawa region.

Given the results found obtained from this sample, the researchers are able to build the following confidence interval (at a 95% confidence level) for the importance given to “environmental issues”:

C.I. = 3.41 ± 0.80, or (stated differently): [2.61 ; 4.21]

1. Giventhat the width of the confidence interval is rather large, the researchers decide to modify the level of confidence that they wish to have for their interval. If they want to narrow their interval, what should they do to this level of confidence?

The researchers would like to push their investigation further and be able to compare how populations from cities across the country view these issues. To compare with their Ottawa respondents, they conduct the same survey in Toronto and Montreal, with a sample selected from each city.

The researchers have a simple hypothesis: that people have, on average, a different opinion on each of these issues, depending on which city they live in (Ottawa, Toronto or Montreal).

They look first at the descriptive statistics for the “environmental issues”, for respondents in Toronto vs. Ottawa:

Given the means for each sample, the researchers decide to conduct a one-tailed t test, using as a research hypothesis the proposition that the mean for Toronto is larger than the mean for Ottawa.

The results for the t-test are as follows:

1. Lookingat the results, what can you conclude on the research hypothesis? Be

Now consider the following results. The researchers are interested in the two-tailed t-test conducted with the groups of cases from Ottawa and Montreal.

1. State the two versions of the criteria required to “pass” the two-tailed test (i.e., to reject thenull hypothesis).
2. With an alpha = 0.05, is the difference between the groups’ means statistically significant?
3. Sincethe researchers would like to consider all three cities at the same time (and perhaps other cities as well), they would like to consider if a Chi-Squared test can be applied  Looking at the two variables, is it possible conduct a Chi-Square in this context? Be specific but concise.

Researchers would like to determine the main drivers of human development around the world. Using statistical data, they compile information on a random sample of 37 countries where development is measured with the Human Development Index, which measures the level of development on a continuous scale ranging from 0 (very low) to 1 (very high).

The independent variables included in the model are described in the table below.

The indicators can all be considered to be interval/ratio level, with the exception of the CONFLICT variable which is dichotomous (0 or 1).

Here are the results from a multivariate regression they conducted on one of the samples: