A research study is conducted to test the effectiveness of a new itching cream. A group of 1000 patients are randomly divided into two groups: group A is given the new medicine while the group B is given a placebo. The patients do not know which group they belong to, and neither do the evaluators/assessors as they interview them about the level of itchiness. What type of research study is this?

As California implemented the “mandatory mask” policy in Spring 2020, the number of new coronavirus cases started to go down for a few months.  What does this say about the “mandatory mask” policy and its effective in slowing down the coronavirus infection in the state of California?

As L.A. County implemented the “Safer at Home” policy, the number of new coronavirus cases started to go down.  What does this say about the “Safer at Home” policy and its effective in slowing down the coronavirus infection in L.A. county?

You got a 20% discount on an event ticket and paid $50 for it. The original ticket price was $62.50.

Suppose you are financing $300,000 to buy a house. The amount of your monthly payment will be more with a 15-year mortgage compared with a 30-year mortgage. 

A factory manufactures tens of thousands of screws every day. A quality control person inspects every 100th screw to be sure that the dimensions are correct. What type of sampling is this?

Suppose that the diameter of a baseball is 3 inches while the diameter of a softball is 3.5 inches. By what percent is the volume of the softball bigger than the volume of the baseball? (You do not need any volume formulas for this question.)  On your paper, show your work and answer. Write only your answer below, but YOUR ANSWER AND WORK SHOULD BE ON YOUR PAPER. 

Three coins are tossed. Find the probability that you get EXACTLY one Heads. (That’s one Heads and two Tails in any order.) Write ONLY your answer in the response box. Show your work which justifies your answer ON YOUR PAPER.

Five people went to the same DMV office and recorded how long they had to wait to be served (in minutes). The results are as follows:  55, 78, 40, 40, 37 Find the mean, the median, and the mode. Be sure to find all three and indicate which one is which. Write ONLY your answers in the response box. Show your work which justifies your answers ON YOUR PAPER.

An ice cream shop has 7 flavors to choose from. If you can pick 2 different flavors (assume the order is not important), in how many ways can you choose your 2 flavors?