The Indonesian government from all of its schools with 11th graders selected 26 schools via a simple random sample. The number of 11th grade students enrolled in each school across the country was 125. At these 26 schools at the beginning (ie, September) and also again at the end (ie, June) of an academic year all 11th grade students were tested on their knowledge about fundamental and technical analysis of equity securities. During that academic year throughout the country students stayed at their school and no new students joined a school.

Inspired by the efforts of the Indonesian government, the Nepalese government does the same but its simple random sample contains 32 schools. Just like in Indonesia, during that academic year throughout Nepal students stayed at their school and no new students joined a school. The number of 11th grade students per school was also 125.

Not having suitable analytical skills themselves, the two governments join forces and hire your analytic consulting company to analyze the data of student performances. Because of your MBA degree and the high-quality analytic staff you have hired after you graduated from St Mary's College of California, you charge the government $120,000 for your service.

The test score sample statistics across the schools per country and month are as follows:

Country	Month	Number of Schools	Sample Mean	Sample Standard Deviation
Indonesia	September	26	13.9	5.2
June	14.8	5.9
Nepal	September	32	14.1	4.9
June	14.9	6.2

So, for example, in Nepal in September the average score of the 32 schools was 14.1 and the standard deviation across those 32 schools was 4.9.

1. Say in the data your analyst looks at the June test scores of individual schools in Indonesia.
   1. Data from what country and month would be needed so that together with the Indonesian June data a "matched sample" is then available for analysis?
   2. On the other hand, data from what country and month would be needed so that now he then has two "independent samples" to work with?
2. Compare these two countries' true mean school scores at the beginning of the school year:
   1. Calculate the 80% confidence interval of the difference in true mean school scores
   2. Test at the 2% level of significance that the true mean school scores of the countries are the same versus not the same. Also include the p-value of this test (either the exact value or [when using a table in the textbook] a lower bound).
   3. Regarding (b), what is the probability to commit a Type 1 error? Assume here your null hypothesis is true.
   4. If Type 1 error does happen in (b), what does this mean for the countries and their schools?