Certain regions of the world are associated with Upper or Lower income groups. For instance:

• Upper-income countries are predominantly located in regions like Western Europe, North America, and parts of East Asia (e.g., Japan, South Korea).
• Low-income countries are often found in Sub-Saharan Africa or South Asia

Can you validate this belief using the provided data ?

Focus only on the Upper income countries!

We want to test Ho: π≥0.4 vs H1:π<0.4 using α=0.05.

where π represents the proportion of Upper income countries with Infant mortality rate above 3.

What is your conclusion ?

Do you think that Infant mortality rate relates with Population density ?

Use this model 

If needed use α=0.05.

Infant mortality rate and GDP per capita are related: an inverse relationship between these two indicators, where countries with higher GDP per capita tend to have lower Infant mortality rates.

You can check what the provided data is expressing about this.

To find out if the sample is providing statistical evidence to validate the above described belief we want to do it using a Contingency Analysis.

What is your expectation for Q if you consider a common α?

Do you think Infant mortality rate is Income group dependent (use α=0.01)?

Focus on Infant mortality rate and consider α=0.10.

The Margin of Error for μ 

The previous model was modified:

(the same sample was considered)

What are your conclusions using a 0.10 level of significance ?

Still about this model (and using the same sample)

Income Group was considered as explanatory (as dummy variables):

(the same sample was considered)

What are your conclusions using a 0.10 level of significance ?

This model was considered to investigate if Infant mortality rate (IMR) is GDP per capita (GDP) related:

.

Using the sample described in the beginning of the Exam, the coefficient of correlation was computed and found to be -0.674.

Ho: R²=0 was tested.

The p-value is