This process of presenting two sets of hypotheses has long been used in the courts. For instance, when a person accused of some crime is presented in the court, he or she by default is considered “innocent” (remember innocent until proven guilty). This consideration is nothing but the Null hypotheses. The alternative hypothesis, on the other hand, is that the person is not innocent (or guilty).
So, H0: Person is innocent
H1: Person is not innocent
The main idea here is that we will work with H0 and see if there is enough evidence presented in favor of or against H0. Based on the evidence presented, if the jury is convinced that H0 does not hold or in other words that the person is not innocent, we can conclude that H0 is rejected and H1 is accepted.
By comparison, if the jury is not convinced and finds that insufficient evidence has been presented, H0 is supported; implying that the person is innocent. And, H1 is rejected.
In this assignment, please carefully read the problem statements before you write hypotheses.
In the next section, I provide four problem statements and your task is to write H0 and H1 both in sentence and mathematical forms. I have provided three examples as well. Please follow the same format for your answers. Please search for keywords such as difference, increase, reduce, low, etc. This will guide you to identify if the hypotheses are two-tail or one-tail (upper or lower).
Example 1: Martina’s company would like to test if they hire more female employees than male employees.
The first thing you need to look for is the keyword “more.” It implies that it is a One-tail test. And since it is asking for more, it is an upper tail test.
Please use the following format to answer your responses:
Type of test: One-tail (Upper)
Hypotheses in sentence form:
H0: The Company does not hire more female employees than male employees
H1: The Company hires more female employees than male employees
Hypotheses in mathematical form
H0: F ≤ M
H1: F > M
Where M represents the population mean of the number of male hires in the company and F represents the population mean of the number of female hires in the company
(Please note that, while writing hypotheses in mathematical form, you would need to define your notations such as F and M)
Example 2: The Tylenol Company claims that its each “Tylenol Extra Strength Caplets” contains 325 milligrams of acetaminophen. However, a group of pharmacists disagrees with them and would like to test the Company’s claim.
In other words, according to the pharmacists each “Tylenol Extra Strength Caplets” does not contain 325 milligrams of acetaminophen.
Type of test: Two-tail; this is because the pharmacists can invalidate the Company’s claim by suggesting that each “Tylenol Extra Strength Caplets” contains either more or less than 325 milligrams of acetaminophen
Hypotheses in sentence form:
H0: Each “Tylenol Extra Strength Caplets” contains 325 milligrams of acetaminophen
H1: Each “Tylenol Extra Strength Caplets” does not contain 325 milligrams of acetaminophen
Hypotheses in mathematical form
H0: A = 325
H1: A ≠ 325
Where A represents the population mean of the amount of acetaminophen in each Tylenol Extra Strength Caplets.
Example 3: A hospital would like to test if the doctors with a medical degree from School 1 earn less than those with a degree from School 2.
Type of test: One-tail (Lower); Keyword = earn less
Hypotheses in sentence form:
H0: Doctors with a medical degree from School 1 do not earn less than those with a degree from School 2
H1: Doctors with a medical degree from School 1 earn less than those with a degree from School 2
Hypotheses in mathematical form
H0: School 1 (salary) ≥ School 2 (salary)
H1: School 1(salary) < School 2 (salary)
Where School 1 (salary) represents the population mean of the salaries of the doctors with a medical degree from School 1 and School 2 (salary) represents the population mean of the salaries of the doctors with a medical degree from School 2.
Please find assignment problem statements below for which you need to write hypotheses:
Module 5 - Assignment
Here are the four scenarios that you will need to answer yourself for the assignment. Please write H0 and H1 both in sentence and mathematical forms. Please use the answer format showed in the examples problem above.
1. Let us say a student wants to test the instructor’s claim that whatever class he teaches the students on average get a GPA of 3.5.
2. Let us say someone wants to test that the average tax savings in 2016 for the State of Florida residents was more than $1,500.
3. Let us say a pharmacist wants to test whether Mucinex DM contains less than 1200 mg of Guaifenesin.
4. Let us say a pharmacist wants to test whether ZYRTEC-D contains 5 mg of cetirizine hydrochloride.
4