Hi! So, yours is actually a sophisticated question that masquerades as a simple one, so I'll try to answer this in a way that conveys the concept while perhaps alluding to some of its problems. At its heart, the null hypothesis is a sort of "straw man" that is defined by a researcher at the beginning of an experiment that usually represents a state of affairs that would be expected to occur if the researcher's proposal were false. Note that a null hypothesis is entirely imaginary, and it has nothing to do with the actual state of the world. It is contrived, usually to show that the actual state of the world is inconsistent with the null hypothesis. Suppose a researcher is trying to determine whether the heights of men and women are different. A suitable null hypothesis might be that the difference of the two population averages (height of men and height of women) is equal to zero. Then the researcher would conduct his or her experiment by measuring the heights of many men and women. When it comes time to draw a statistical conclusion, he or she will compute the probability that the observed data (the set of heights) could have come from the null hypothesis (i.e., a world where there is no difference). This probability is called a "p-value". Conceptually, this is similar to a "proof by contradiction," in which we assert that, if the probability is very small that the data could have originated from the null hypothesis, it must not be true. This is what is meant by "rejecting the null hypothesis". It is different from a proof by contradiction because rejecting the null proves nothing, except perhaps that the null is unlikely to be the source of the observed data. It doesn't prove that the true difference is 5 inches, or 1 inch, or anything. Because of this, rejecting the null hypothesis is in NO WAY equivalent to accepting an alternative hypothesis. Usually, in the course of an experiment, we observe a result (such as the observed height difference, perhaps it is ~5 inches) that, once we reject, replaces the hypothesized value of 0 under the null. However, we DON'T know anything about the probability that our observed value is "correct", which is why we never say that we have "accepted" an alternative. I actually hesitate to discuss an "alternative" hypothesis because most researchers never state one and it doesn't matter for the purposes of null hypothesis significance testing (NHST). It is just the name given to the conclusion drawn by the researchers after they have rejected their null hypothesis. Philosophically, there is an adage that data can never be used to prove an assertion, only to disprove one. It includes an analogy about a turkey concluding that he is loved by his human family and is proven wrong upon being slaughtered on Thanksgiving. I'll include a link if I can find it. Now, think about this: The concept of rejecting a null hypothesis probably seems very reasonable as long as we are careful not to overinterpret it, and this is how NHST was performed for decades. But consider - what is the probability that the null hypothesis is true in the first place? In other words, how likely is it that the difference between mens' and womens' heights is equal to zero? I propose that the probability is exactly zero, and if you disagree then I will find a ruler small enough to prove me correct. The difference can never be equal to exactly zero (even though this is the "straw man" that our experiment refutes), so we are effectively testing against a hypothesis that can never be true. Rejecting a hypothesis we already know to be false tells us nothing important ("the data are unlikely to have come from this state that cannot be true"). And since every null hypothesis is imaginary, it is suggested that any null hypothesis can be rejected with enough statistical power (read:sample size). Often a "significant" result says more about a study's sample size than it does about the study's findings, even though the language used in papers/media suggests to readers that the findings are more "important" or "likely to be correct". This has, in part, led to a reproducibility crisis in the sciences and, for some, an undermining of subject-matter-experts' trust in the use of applied statistics. Answer from stat_daddy on reddit.com
National University
resources.nu.edu › statsresources › hypothesis
Null & Alternative Hypotheses - Statistics Resources - LibGuides at National University
October 27, 2025 - Alternative Hypothesis: Ha: Male factory workers have a higher salary than female factory workers. Null Hypothesis: H0: There is no relationship between height and shoe size.
Quora
quora.com › What-are-some-examples-of-null-hypothesis-and-its-corresponding-alternative-hypothesis
What are some examples of null hypothesis and its corresponding alternative hypothesis? - Quora
Answer (1 of 3): These are statistical terms and are used only for statistical analysis. In statistics there is the population and there are the samples. The population is an idealized group of every example in every place through all of time. Say we are going to compare healing times of intrame...
Null hypothesis and Alternative Hypothesis
Hi! So, yours is actually a sophisticated question that masquerades as a simple one, so I'll try to answer this in a way that conveys the concept while perhaps alluding to some of its problems. At its heart, the null hypothesis is a sort of "straw man" that is defined by a researcher at the beginning of an experiment that usually represents a state of affairs that would be expected to occur if the researcher's proposal were false. Note that a null hypothesis is entirely imaginary, and it has nothing to do with the actual state of the world. It is contrived, usually to show that the actual state of the world is inconsistent with the null hypothesis. Suppose a researcher is trying to determine whether the heights of men and women are different. A suitable null hypothesis might be that the difference of the two population averages (height of men and height of women) is equal to zero. Then the researcher would conduct his or her experiment by measuring the heights of many men and women. When it comes time to draw a statistical conclusion, he or she will compute the probability that the observed data (the set of heights) could have come from the null hypothesis (i.e., a world where there is no difference). This probability is called a "p-value". Conceptually, this is similar to a "proof by contradiction," in which we assert that, if the probability is very small that the data could have originated from the null hypothesis, it must not be true. This is what is meant by "rejecting the null hypothesis". It is different from a proof by contradiction because rejecting the null proves nothing, except perhaps that the null is unlikely to be the source of the observed data. It doesn't prove that the true difference is 5 inches, or 1 inch, or anything. Because of this, rejecting the null hypothesis is in NO WAY equivalent to accepting an alternative hypothesis. Usually, in the course of an experiment, we observe a result (such as the observed height difference, perhaps it is ~5 inches) that, once we reject, replaces the hypothesized value of 0 under the null. However, we DON'T know anything about the probability that our observed value is "correct", which is why we never say that we have "accepted" an alternative. I actually hesitate to discuss an "alternative" hypothesis because most researchers never state one and it doesn't matter for the purposes of null hypothesis significance testing (NHST). It is just the name given to the conclusion drawn by the researchers after they have rejected their null hypothesis. Philosophically, there is an adage that data can never be used to prove an assertion, only to disprove one. It includes an analogy about a turkey concluding that he is loved by his human family and is proven wrong upon being slaughtered on Thanksgiving. I'll include a link if I can find it. Now, think about this: The concept of rejecting a null hypothesis probably seems very reasonable as long as we are careful not to overinterpret it, and this is how NHST was performed for decades. But consider - what is the probability that the null hypothesis is true in the first place? In other words, how likely is it that the difference between mens' and womens' heights is equal to zero? I propose that the probability is exactly zero, and if you disagree then I will find a ruler small enough to prove me correct. The difference can never be equal to exactly zero (even though this is the "straw man" that our experiment refutes), so we are effectively testing against a hypothesis that can never be true. Rejecting a hypothesis we already know to be false tells us nothing important ("the data are unlikely to have come from this state that cannot be true"). And since every null hypothesis is imaginary, it is suggested that any null hypothesis can be rejected with enough statistical power (read:sample size). Often a "significant" result says more about a study's sample size than it does about the study's findings, even though the language used in papers/media suggests to readers that the findings are more "important" or "likely to be correct". This has, in part, led to a reproducibility crisis in the sciences and, for some, an undermining of subject-matter-experts' trust in the use of applied statistics. More on reddit.com
18
18
January 5, 2021[College Statistics] Help with null/alternative hypothesis?
Hey! Really good questions. Rather than just answer you, I think it's important to explain definitions and why we need to ask for null/alternative hypotheses in statistics. First, in stats, we are trying to find mathematical grounds for believing there is an actual relationship or association between some phenomena. In your example: grocery prices at Walmart and grocery prices at Target. Your hypothesis, Walmart has cheaper groceries than Target, is the alternative hypothesis. Now, I know what you're thinking! What, how can this be? That is my hypothesis, not an alternative! Which is true, but hold on.
Second, when searching for evidence of this (or any) relationship, you are attempting to disprove or reject the null hypothesis, which sounds weirder than it is. "Null" means no significance, no relationship. This is the default position, where there is no relationship between the prices at Walmart and the prices at Target. Thus, the alternative is that there is some relationship. If your data reveal an association, you reject the null hypothesis; if analyses reveal no relationship between prices, you would not reject the null hypothesis. In stats, neither theory is "proven," but data must be analyzed and interpreted to determine how statistically significant, or likely/unlikely, the data are.
As for what test to run, I think you should use a "difference in means" hypothesis test, or a t-test. To do this, you'll need to pick your significance level (.01, .05, .10 are common, if you've been using one in class, go with that), and compute the standard deviation of each of the two samples (prices at (1) Walmart and (2) Target), the standard error, degrees of freedom, and t-value. With the t-value, you can calculate the P-value. This reflects the probability of finding a relationship as extreme as your data assuming the null is true. For example, if your P-value is p=.03, it indicates that if Walmart's prices are the same as Target's, one could expect to obtain your observed difference or more in 3% of studies due to random sampling error.
This website is a great resource. I hope this helps! Feel free to PM me if you have any questions. :)
More on reddit.com 3
2
June 6, 2016[Q] Question about choosing null and alternative hypotheses
The null is ALWAYS the opposite of what you want to prove. It is related to modus tollens. If A then B and Not B therefore not A. More on reddit.com
26
36
April 9, 2023Null and alternative Hypothesis statement
I don't see any reason why you're going for a one-sided hypothesis in the first place? It looks like you're trying to base your hypothesis on the results of the data, which is a huge misstep.
Unless you have more information you're not sharing with us, I don't see any reason why you would use anything besides the usual two-tailed Ha: p1 =/= p2
More on reddit.com 5
4
March 17, 2016Videos
14:52
Null and Alternate Hypothesis - Statistical Hypothesis Testing ...
Examples of null and alternative hypotheses (video)
03:49
Null and alternative hypotheses with Lindsey Leach - YouTube
14:38
Writing the Null and Alternate Hypothesis in Statistics - YouTube
04:35
Null Hypothesis Vs Alternative Hypothesis (Easy Explanation) - YouTube
Hypothesis Testing EXPLAINED
Statistics LibreTexts
stats.libretexts.org › campus bookshelves › las positas college › math 40: statistics and probability › 8: hypothesis testing with one sample › 8.1: steps in hypothesis testing
8.1.1: Null and Alternative Hypotheses - Statistics LibreTexts
August 8, 2020 - Bring to class a newspaper, some news magazines, and some Internet articles . In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class. In a hypothesis test, sample data is evaluated in order to arrive at a decision about some type of claim.
Lumen Learning
courses.lumenlearning.com › introstats1 › chapter › null-and-alternative-hypotheses
Null and Alternative Hypotheses | Introduction to Statistics
The null statement must always ... the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis. Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties. H0 and Ha are contradictory. ... OpenStax, Statistics, Null and ...
Pressbooks
ecampusontario.pressbooks.pub › introstats › chapter › 8-2-null-and-alternative-hypotheses
8.2 Null and Alternative Hypotheses – Introduction to Statistics
September 1, 2022 - On a state driver's test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. State the null and alternative hypotheses. ... In a hypothesis test, sample data is evaluated in order to arrive at a decision about some type of claim.
Reddit
reddit.com › r/askstatistics › null hypothesis and alternative hypothesis
r/AskStatistics on Reddit: Null hypothesis and Alternative Hypothesis
January 5, 2021 -
Hey! Can someone explain to me in simple terms the definition of null hypothesis? If u can use an example it would be great! Also if we reject the null hypothesis does it mean that the alternative hypothesis is true?
Top answer 1 of 4
30
Hi! So, yours is actually a sophisticated question that masquerades as a simple one, so I'll try to answer this in a way that conveys the concept while perhaps alluding to some of its problems. At its heart, the null hypothesis is a sort of "straw man" that is defined by a researcher at the beginning of an experiment that usually represents a state of affairs that would be expected to occur if the researcher's proposal were false. Note that a null hypothesis is entirely imaginary, and it has nothing to do with the actual state of the world. It is contrived, usually to show that the actual state of the world is inconsistent with the null hypothesis. Suppose a researcher is trying to determine whether the heights of men and women are different. A suitable null hypothesis might be that the difference of the two population averages (height of men and height of women) is equal to zero. Then the researcher would conduct his or her experiment by measuring the heights of many men and women. When it comes time to draw a statistical conclusion, he or she will compute the probability that the observed data (the set of heights) could have come from the null hypothesis (i.e., a world where there is no difference). This probability is called a "p-value". Conceptually, this is similar to a "proof by contradiction," in which we assert that, if the probability is very small that the data could have originated from the null hypothesis, it must not be true. This is what is meant by "rejecting the null hypothesis". It is different from a proof by contradiction because rejecting the null proves nothing, except perhaps that the null is unlikely to be the source of the observed data. It doesn't prove that the true difference is 5 inches, or 1 inch, or anything. Because of this, rejecting the null hypothesis is in NO WAY equivalent to accepting an alternative hypothesis. Usually, in the course of an experiment, we observe a result (such as the observed height difference, perhaps it is ~5 inches) that, once we reject, replaces the hypothesized value of 0 under the null. However, we DON'T know anything about the probability that our observed value is "correct", which is why we never say that we have "accepted" an alternative. I actually hesitate to discuss an "alternative" hypothesis because most researchers never state one and it doesn't matter for the purposes of null hypothesis significance testing (NHST). It is just the name given to the conclusion drawn by the researchers after they have rejected their null hypothesis. Philosophically, there is an adage that data can never be used to prove an assertion, only to disprove one. It includes an analogy about a turkey concluding that he is loved by his human family and is proven wrong upon being slaughtered on Thanksgiving. I'll include a link if I can find it. Now, think about this: The concept of rejecting a null hypothesis probably seems very reasonable as long as we are careful not to overinterpret it, and this is how NHST was performed for decades. But consider - what is the probability that the null hypothesis is true in the first place? In other words, how likely is it that the difference between mens' and womens' heights is equal to zero? I propose that the probability is exactly zero, and if you disagree then I will find a ruler small enough to prove me correct. The difference can never be equal to exactly zero (even though this is the "straw man" that our experiment refutes), so we are effectively testing against a hypothesis that can never be true. Rejecting a hypothesis we already know to be false tells us nothing important ("the data are unlikely to have come from this state that cannot be true"). And since every null hypothesis is imaginary, it is suggested that any null hypothesis can be rejected with enough statistical power (read:sample size). Often a "significant" result says more about a study's sample size than it does about the study's findings, even though the language used in papers/media suggests to readers that the findings are more "important" or "likely to be correct". This has, in part, led to a reproducibility crisis in the sciences and, for some, an undermining of subject-matter-experts' trust in the use of applied statistics.
2 of 4
6
The null hypothesis (Ho) signifies no change. The alternative hypothesis (Ha) signifies a change. If we reject the null, we have evidence for the alternative hypothesis. This doesn’t mean that it’s true just that within this study, we have evidence to support the alternative hypothesis. If we fail to reject the null (we don’t use the word accept) then there is not enough evidence supporting the alternative hypothesis. Example: I’m wondering if smoking impacts lung function using a spirometry test that measures forced exploratory volume per second (FEV1). Ho: There is no difference in FEV1 between smokers vs non smokers Ha: There is a difference in FEV1 between smokers and non smokers. Rejecting or failing to reject the null aka Ho will involve more steps than just analyzing the mean FEV1 between the two groups, so let’s stop here before we get into more hypothesis testing.
Outlier
articles.outlier.org › null-vs-alternative-hypothesis
Null vs. Alternative Hypothesis [Overview] | Outlier
April 28, 2023 - One hypothesis is that the proportion of vegetarians is 5%. The other hypothesis is that the proportion of vegetarians is greater than 5%. In statistics, we would call the first hypothesis the null hypothesis, and the second hypothesis the ...
Tallahassee State College
tsc.fl.edu › media › divisions › learning-commons › resources-by-subject › math › statistics › The-Null-and-the-Alternative-Hypotheses.pdf pdf
The Null and the Alternative Hypotheses
more than or less than 50%. The Null and Alternative Hypotheses looks like: H0: p = 0.5 (This is ... They want to test what proportion of the parts do not meet the specifications. Since they claim · that the proportion is less than 2%, the symbol for the Alternative Hypothesis will be <. As is the
Slideshare
slideshare.net › home › data & analytics › null and alternative hypothesis.pptx
NULL AND ALTERNATIVE HYPOTHESIS.pptx
It is represented by H1 or Ha. If the null hypothesis is rejected based on a low p-value, the alternative hypothesis is supported, meaning the results are statistically significant. Examples of null and alternative hypotheses are provided. - Download as a PPTX, PDF or view online for free
Wisc
biostat.wisc.edu › ~kendzior › STAT541 › lc11.short.pdf pdf
1 Hypothesis testing
A two-sided alternative · hypothesis is just a negation of the null hypothesis, allowing for the · population parameter to be either larger or smaller than the value ... Here, the p-value is 0.0198. Consider α = 0.05 (zα/2 shown in blue), H0 is rejected since p-value · is less than α. We conclude that physicians, on average, are under ... The form of the test statistic has not changed.
Pressbooks
ecampusontario.pressbooks.pub › sccstatistics › chapter › null-and-alternative-hypotheses
Chapter 9.2: Null and Alternative Hypotheses – College Statistics
July 1, 2022 - H0: No more than 30% of the registered ... voted in the primary election. p > 30 ... A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypothes...
Scribbr
scribbr.com › home › null and alternative hypotheses | definitions & examples
Null and Alternative Hypotheses | Definitions & Examples
January 24, 2025 - Alternative hypotheses often include phrases such as “an effect,” “a difference,” or “a relationship.” When alternative hypotheses are written in mathematical terms, they always include an inequality (usually ≠, but sometimes < or >). As with null hypotheses, there are many acceptable ways to phrase an alternative hypothesis. The table below gives examples of research questions and alternative hypotheses to help you get started with formulating your own. Null and alternative hypotheses are similar in some ways: They’re both answers to the research question. They both make claims about the population. They’re both evaluated by statistical tests.
Investopedia
investopedia.com › terms › n › null_hypothesis.asp
Null Hypothesis: What Is It and How Is It Used in Investing?
May 8, 2025 - Failing to reject the null ... for the statistical test to detect them. An important point to note is that we are testing the null hypothesis because there is an element of doubt about its validity. Whatever information that is against the stated null hypothesis is captured in the alternative (alternate) hypothesis (H1). For the examples below, the ...
Nc3rs
eda.nc3rs.org.uk › experimental-design-experiment
Understanding your experiment | NC3Rs EDA
For example, if the effect of a proposed anti-cholesterol drug on blood pressure is being tested, then the null hypothesis could be that the drug treatment has no effect on the measured blood pressure: H0: The anti-cholesterol drug has no effect – there are no differences among treatment ...
Laerd Statistics
statistics.laerd.com › statistical-guides › hypothesis-testing-3.php
Hypothesis Testing - Significance levels and rejecting or accepting the null hypothesis
Typically, if there was a 5% or less chance (5 times in 100 or less) that the difference in the mean exam performance between the two teaching methods (or whatever statistic you are using) is as different as observed given the null hypothesis is true, you would reject the null hypothesis and accept the alternative hypothesis. Alternately, if the chance was greater than 5% (5 times in 100 or more), you would fail to reject the null hypothesis and would not accept the alternative hypothesis. As such, in this example where p = .03, we would reject the null hypothesis and accept the alternative hypothesis.
Simplilearn
simplilearn.com › home › resources › data science & business analytics › the ultimate statistics tutorial › hypothesis testing in statistics - types | examples
Hypothesis Testing: Types, Steps, Formula, and Examples
4 weeks ago - Hypothesis testing is a statistical method used to determine if there is enough evidence in a sample data to draw conclusions about a population.
Applied Mathematics
colorado.edu › amath › sites › default › files › attached-files › lesson9_hyptests.pdf pdf
9 Hypothesis Tests (Ch 9.1-9.3, 9.5-9.9)
Test statistic value: z = 48 · Test Procedures for Normal Populations with Known Variances · Null hypothesis: H0: µ1 – µ2 = Δ0 · Alternative Hypothesis Rejection Region for Level α Test · Ha: µ1 – µ2 > Δ0 z ≥zα (upper-tailed) Ha: µ1 – µ2 < Δ0 z ≤– zα (lower-tailed) Ha: µ1 – µ2 ≠ Δ0 either z ≥zα/2 or z ≤– zα/2(two- · tailed) 49 · Example 1 ·
Penn State Statistics
online.stat.psu.edu › stat502 › lesson › 1 › 1.2
1.2 - The 7 Step Process of Statistical Hypothesis Testing | STAT 502
To cover all alternative outcomes, ... In our example, a possible outcome would be that fertilizer 1 results in plants that are exceptionally tall, but fertilizers 2, 3, and the control group may not differ from one another....
GeeksforGeeks
geeksforgeeks.org › software testing › understanding-hypothesis-testing
Hypothesis Testing - GeeksforGeeks
Null Hypothesis: (H0)The new drug has no effect on blood pressure. Alternate Hypothesis: (H1)The new drug has an effect on blood pressure. Usually 0.05, meaning less than 5% chance results are by random chance.
Published July 28, 2025