Question

(b) Professor GeniusAtCalculus has two lecture sections (A and B) of the same 4th year
Advanced Calculus (AMA 4301) course in Semester 2. She wants to investigate whether
section A students maybe ”smarter” than section B students by comparing their performances in the midterm test. A random sample of 12 students were taken from section
A, with mean midterm test score of 78.8 and standard deviation 8.5; and a random
sample of 9 students were taken from section B, with mean midterm test score of 86
and standard deviation 9.3. Assume the population standard deviations of midterm test
scores for both sections are the same. Construct the 90% confidence interval for the
difference in midterm test scores of the two sections. Based on the sample midterm test
scores from the two sections, can Professor GeniusAtCalculus conclude that there is any
evidence that one section of students are ”smarter” than the other section? Justify your
conclusions.
[8 marks]

(c) The COVID-19 (coronavirus) mortality rate of a you country is defined as the ratio of the
number of deaths due to COVID-19 divided by the number of (confirmed) cases of
COVID-19 in that country. Suppose we want to investigate if there is any difference
between the COVID-19 mortality rate in the US and the UK. On April 18, 2020, out of
a sample of 671,493 cases of COVID-19 in the US, there was 33,288 deaths; and out of
a sample of 109,754 cases of COVID-19 in the UK, there was 14,606 deaths. What is
the 92% confidence interval in the true difference in the mortality rates between the two
countries? What can you conclude about the difference in the mortality rates between
the US and the UK? Justify your conclusions. [8 marks]

Answer 1