Question

In Chapter 10 you study two different types of hypothesis​ tests:
-Claim about a Population Proportion
-Claim about a Population Mean

An example of each is given below. For each​ one, state which type of test it​ is, define the parameter in​ question, and write the null hypothesis for the test symbolically​ (use the math palette if necessary for appropriate​ symbols).

​(a) A research hospital tries a new antibiotic scrub before surgery to see whether it can lower the rate of infections of surgical sites. The old rate of infection is​ 4%. A sample of 600 surgeries with the new scrub shows 18 infections. Test the claim that new scrub lowers the rate of infection.

​(b) The Old​ Farmer's Almanac stated that the average consumption of water per person per day was 123 gallons. To test the hypothesis that this figure may no longer be​ true, a researcher randomly selected 16 people and found that they used on average 119 gallons per day with a standard deviation of 5.3 gallons per day. Is there evidence that the Old​ Farmer's Almanac might no longer be​ correct?

For​ (a) and for​ (b) state which type of test it and explain by defining the parameter in question. Than write the null hypothesis symbolically. ​ Note: You are NOT being asked to do the math to conduct a full hypothesis test. Just do the three things you are told to do.

Answer 1

a)

type of test - Hypothesis test for one proportion

parameter is rate of infection of surgical sites

hypothesis used

Ho :   p =    0.04
H1 :   p <   0.04

b)

type of test: Hypothesis test for one mean

parameter: average consumption of water per person per day

Hypothesis used:

Ho :   µ =   123
Ha :   µ ╪   123