The economic dynamism, which is the index of productive growth in dollars for countries that are designated by the World Bank as middle-income are in the table below. Countries that are considered high-income have a mean economic dynamism of 60.29.

Table: Economic Dynamism ($) of Middle Income Countries

(a) Set up and run a test of hypotheses to determine if the data show that the mean economic dynamism of middle-income countries is less than the mean for high-income countries? Use a level of significance of 5%. Specifically, do the following:

(i) Write down the null and alternative hypotheses.

(ii) Verify that the assumptions necessary to apply the test are satisfied.

(iii) What is the test statistic and what is the p-value?

(iv) State your conclusion.

(b) Using the data in the table which represents the index of productive growth in dollars for countries that are designated by the World Bank as middle-income, construct a 95% confidence interval for the true mean economic dynamism of middle-income countries. Make sure to check the assumptions necessary to construct the interval.  Interpret the interval.