Creating Hypotheses
*Note: this guide may use symbols you aren’t familiar with. View our complete list of Statistics Symbols here.
A hypothesis is a claim (also referred to as “assumption” “educated guess” or “explanation”) is based on something that has been observed. It is an idea that can be tested for significance, much like a good argument.
Consider an astronaut. She wants to measure whether or not she’s using more oxygen in her space suit. She would need to know how much oxygen she normally uses as a baseline, to measure any changes against. When she tries to test for change or difference, she must create a hypothesis.
Null hypothesis
The null is a baseline measurement or proportion of whatever it is you’re studying. It will always include an equal sign. The word ‘null’ means zero. Here, for hypothesis testing, we read it as no change. This is usually an expected value based on previous experiments/survey. Originally, we assume this value has not changed. So, for our astronaut, she would assume no change in oxygen, or the null. Other ways of defining a null hypothesis: “no difference,” “original information,” “Currently accepted value of a parameter.”
Alternate hypothesis
Ha or H1 is a statement of comparison. It is the new idea to be tested; i.e., the astronaut is going to test a change in the level of oxygen that she thinks she’s using. It’s a claim based on a new, more recent samples or research whose results look different from the null hypothesis. The alternate is used to test to see if they are truly different enough to be significant. It will oppose what the null states and will have the ‘>’, ‘<’ or ≠ sign
*Note: the signs are opposite! The null always has the equal sign
Example
H0: μ = current oxygen level Ha: μ ≠ current oxygen level
Now You Try! Practice Problems
Example One
Studies show that 40% of adults snooze their alarms at least 3 times before they wake up! A recent survey shows that 350 out of 500 people snooze their alarm clocks. Is their sufficient evidence to show that the proportion of people snoozing their alarm clocks has increased over the years?
- Write the null and alternate hypothesis and determine the type of test
Example Two
Healthcare professionals recommend that children get on an average at least one hour of physical activity every day. A recent study showed children having less than an hour of physical activity
- Write the null and alternate hypothesis to test this
Example One Solution
This is a test based on proportions. The clue is the percentage. The first line in the problem tells you the current percentage of adults snooze their alarms at least 3 times before they wake up. This is the current value you need to form your null hypothesis The percentage needs to be converted to a proportion to write the null. Divide 40% by 100 to get the proportion. So, 40/100 is 0.40. Hence your null hypothesis is:
H0: p = 0.40
There are some numbers in the middle of the problem based on recent studies. We don’t need that for writing the null or the alternate. It will be needed when we calculate your results. We have read before that the alternate should be contradicting the null. In the problem we need to look for words like changed, increased, or decreased to determine the sign for the alternate. The problem says that we need to test if the proportion has ‘increased over the years’. Our key word here is ‘increased’. So the alternate should have ‘>’ sign. Hence the alternate hypothesis is:
Ha: p > 0.40
Since the alternate has ‘>’ sign, this is a right tailed test.
Example 2 Solution
This is a problem about means. The clue here is that the problem uses the word “average.” To discover the initial amount we are using to test, the key words are ‘at least one hour’ which means it can be greater than 1. So our null is:
H0: μ ≥ 1
For determining the alternate the key word is ‘less than’. Another clue is that we need to test the opposite of the null hypothesis. Hence the alternate is:
Ha : μ < 1
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