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?

A survey asks 10,000 people what their household annual income is. This data is quantitative.

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?

Find the probability that you will get at least one Tails when you toss 3 coins.

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?

Complete the table below.  Suppose 6% of those who take the COVID-19 test actually have the virus. The test is 90% accurate in identifying those with COVID-19 and those without COVID-19. Out of 1000 people tested, find out how many people will test positive and how many of those are “false positives” (those who test positive but don’t actually have the virus).  Tested Positive Tested Negative Total Actually with COVID-19 [a] [b] 60 Actually without COVID-19 [c] [d] 940 Total [e] [f] 1000 Copy this table on your paper and fill in the blank boxes. Write ONLY your answers in the response box. Show your work which justifies your answers ON YOUR PAPER.

A Jeep Cherokee costs $26,000 while a Ford Explorer costs $33,000. By what percent is the Cherokee cheaper than the Explorer? On your paper, show your work and answer. Write only your answer below, but YOUR ANSWER AND WORK SHOULD BE ON YOUR PAPER. 

The statement “If p, then q” is logically equivalent to the statement “If not p, then not q.”

If the interest is compounded “6% monthly,” it really means that they will calculate and add interest at _________________

Suppose that scores of a certain standardized test is normally distributed with a mean of 60 and a standard deviation of 7. Find the probability that a random score is less than 67. Use the table below. Use a decimal number (for instance, if the probability is 60%, use 0.6).  Write ONLY your answer in the response box. Show your work which justifies your answer ON YOUR PAPER.