A crucial step in null hypothesis testing is finding the likelihood of the sample result if the null hypothesis were true. This probability is called the
p value
. … If there is greater than a 5% chance of a result as extreme as the sample result when the null hypothesis is true, then the null hypothesis is retained.
What is a true null hypothesis?
A null hypothesis is a
type of hypothesis used in statistics that proposes that there is no difference between certain characteristics of a population (or data-generating process)
. For example, a gambler may be interested in whether a game of chance is fair.
How do you know when to accept or reject the null hypothesis?
Set the significance level, , the probability of making a Type I error to be small — 0.01, 0.05, or 0.10. Compare the P-value to .
If the P-value is less than (or equal to)
, reject the null hypothesis in favor of the alternative hypothesis. If the P-value is greater than , do not reject the null hypothesis.
How do you determine the null hypothesis?
H
0
: The null hypothesis: It is a statement of
no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion
. In other words, the difference equals 0.
When you reject the null hypothesis is there sufficient evidence?
we reject the null hypothesis of equal means. There is sufficient evidence
to warrant rejection of the claim that the three samples come from populations with means that are all equal
.
Why do we reject the null hypothesis if/p α?
It indicates strong evidence against the null hypothesis, as
there is less than a 5% probability the null is correct
(and the results are random). Therefore, we reject the null hypothesis, and accept the alternative hypothesis.
How do you reject the null hypothesis in t test?
If
the absolute value of the t-value is greater than the critical value
, you reject the null hypothesis. If the absolute value of the t-value is less than the critical value, you fail to reject the null hypothesis.
How do you write the null hypothesis in symbols?
The null statement must always contain some form of equality (=, ≤ or ≥) Always write the alternative hypothesis, typically denoted with H
a
or H
1
,
using less than, greater than, or not equals symbols
, i.e., (≠, >, or <).
What do you mean if you fail to reject the null hypothesis?
When we fail to reject the null hypothesis when
the null hypothesis is false
. The “reality”, or truth, about the null hypothesis is unknown and therefore we do not know if we have made the correct decision or if we committed an error.
What type of error is made if you reject the null hypothesis when the null hypothesis is actually true?
A type I error (false-positive)
occurs if an investigator rejects a null hypothesis that is actually true in the population; a type II error (false-negative) occurs if the investigator fails to reject a null hypothesis that is actually false in the population.
Does failing to reject the null hypothesis mean the null hypothesis is true?
When we fail to reject the null hypothesis when the null hypothesis
is false
. The “reality”, or truth, about the null hypothesis is unknown and therefore we do not know if we have made the correct decision or if we committed an error. We can, however, define the likelihood of these events.
Can sample evidence prove a null hypothesis is true?
Sample evidence can prove that a null hypothesis is true. The correct answer is
False
because although sample data is used to test the null hypothesis, it cannot be stated with 100% certainty that the null hypothesis is true.
What should you do when α p-value reject the null hypothesis do not reject the null hypothesis?
Set the significance level, , the probability of making a Type I error to be small — 0.01, 0.05, or 0.10. Compare the P-value to . If the P-value is less than (or equal to) , reject the null hypothesis in favor of the alternative hypothesis.
If the P-value is greater than
, do not reject the null hypothesis.
What does p-value .05 mean?
Again: A p-value of less than . 05 means that there
is less than a 5 percent chance of seeing these results
(or more extreme results), in the world where the null hypothesis is true.
What does p-value tell you?
A p-value is
a measure of the probability that an observed difference could have occurred just by random chance
. The lower the p-value, the greater the statistical significance of the observed difference. P-value can be used as an alternative to or in addition to pre-selected confidence levels for hypothesis testing.
How do you reject the null hypothesis with p-value?
If the p-value is less than 0.05
, we reject the null hypothesis that there’s no difference between the means and conclude that a significant difference does exist. If the p-value is larger than 0.05, we cannot conclude that a significant difference exists. That’s pretty straightforward, right? Below 0.05, significant.
