Question

3. Statistics (20%). To estimate the coronavirus infection situation in a city (with large pop- ulation), the researchers randomly sample N people therein and test their body temperatures.

(a) If N = 5 and the tested results are 36.2, 38.9, 39.2, 38.4, 36.8 (◦C). Calculate the sample mean, variance, standard deviation, medium, and range. (10%)

2

(b) If we want to propose a statistical model (i.e., a probability distribution) to reflect peo- ple’s average temperature in this city. How will you design the model? How to approximate the parameters in the model? (5%)

(c) As per a previous study, human body temperatures, denoted as X, satisfy normal distri- bution, where the mean is 37◦C and standard deviation 0.4◦C, i.e., X ∼ N (37, 0.4). Suppose that we test the body temperatures for 16 people in the city whose sample mean turned out to be 37.3◦C. Let’s use μ to denote the expected value of people’s body temperatures in this city and further make a null hypothesis H0: μ = 37◦C. Will you accept H0 at significance level 5% and 10%, respectively? (5%)

Answer 1