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
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
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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?

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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.
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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.
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Wikipedia
en.wikipedia.org › wiki › Alternative_hypothesis
Alternative hypothesis - Wikipedia
October 6, 2025 - In statistical hypothesis testing, the null hypothesis and alternative hypothesis are two mutually exclusive statements. "The statement being tested in a test of statistical significance is called the null hypothesis. The test of significance is designed to assess the strength of the evidence ...
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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
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Hypothesis testing - Why "Fail to reject null hypothesis" instead of "Accepting Alternative Hypothesis" ?
Because not having enough evidence of something doesn't mean that the opposite of that something is necessarily true. More on reddit.com
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What’s the difference between a research hypothesis and a statistical hypothesis?
A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (“x affects y because …”). · A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses. In a well-designed study, the statistical hypotheses correspond logically to the research hypothesis.
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What symbols are used to represent null hypotheses?
The null hypothesis is often abbreviated as H0. When the null hypothesis is written using mathematical symbols, it always includes an equality symbol (usually =, but sometimes ≥ or ≤).
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January 24, 2025 - The alternative hypothesis (Ha) answers “Yes, there is an effect in the population.” · The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population ...
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Null & Alternative Hypotheses - Statistics Resources - LibGuides at National University
October 27, 2025 - Null Hypothesis (H0) – This can be thought of as the implied hypothesis. “Null” meaning “nothing.” This hypothesis states that there is no difference between groups or no relationship between variables.
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Difference between Null and Alternate Hypothesis - GeeksforGeeks
May 18, 2022 - It acts as a compass in the process. Null hypothesis suggests that there is no relationship between the two variables. Null hypothesis is also exactly the opposite of the alternative hypothesis.
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The purpose of the null is to convert a problem from one of inductive reasoning to one of deductive reasoning. The alternative, and the method that preceded it was the method of inverse probability. That method is now generally called Bayesian statistics.

Imagine that you had three scientific hypotheses, denoted a, b, and c. Imagine that the true model is d, but no one has yet to discover this. The world is still flat, white is still a color, and Mercury follows Newton's laws.

A Bayesian test would create three hypotheses, , , and . For a data set that is large enough, you would end up with the hypothesis or the combination of hypotheses that are most likely true. However, since wasn't tested, you may continue to be fooled by the idea yet to be thought of.

The Frequentist hypothesis testing regime would assume that the alternative hypothesis is , and the null is . The null contains every hypothesis that is not the alternative.

The first example in the academic literature, but not the first null hypothesis, is where R.A. Fisher assumed that Mendel's laws were false as the null. If you discredit the null, then you exclude every explanation, including those not yet considered. The first null hypothesis was that Muriel Bristol (Fisher's boss) could not correctly detect the difference between tea poured into mild from milk poured into tea. That was the very first statistical test.

There is a slight difference between R.A. Fisher's idea of a null and Pearson and Neyman's idea of a null. Fisher felt there was a null, but no alternative hypothesis. If you rejected the null, it told you what was wrong, but was not directive as to what was correct automatically. Pearson and Neyman championed acceptance and rejection regions based on frequencies, and they felt the method directed behavior.

The logic was that the method created a probabilistic version of modus tollens. Modus tollens is "if A then B; and, not B; therefore, not A." Or, if the null is true, then the test will appear in the acceptance region if it does not, then you can reject the null.

The weakness of the methodology was proposed by an author that I cannot currently locate in this somewhat tongue-in-cheek way. There are 535 elected members representing the states in the U.S. Congress. There are 360 million Americans. Therefore since 535/360000000 is less than .05, if you randomly sample a group of Americans and pick a member of Congress, they cannot be an American (p<.05).

While Fisher's no effect hypothesis is the most common version, because of its implication would be that something has an effect in the alternative, it is not a requirement that a parameter equals zero, or a set of parameters all equal zero.

What matters is that the null is the opposite of what you are wanting to assert before seeing the data.

That makes the null hypothesis method a potent tool. Think about this as a rhetorical device. Your opponent opposes that you recently believe you have discovered.

You do not assert is true. You assert your opponent's position of is true and build your probabilities on the assumption that you are the only person that is wrong. Everyone is right, and you are wrong.

It is a powerful rhetorical tool to concede the argument from the beginning, but then ask, "what would the world look like if I am the one that is wrong?" That is the null. If you reject the null, then what you are really saying is that "nature rejects all other ideas except mine."

Now as to your question, you want to show that college algebra matters, therefore your null hypothesis is that college algebra does not matter. We will ignore all the other methodological issues that would really be present since people without college algebra may have other self-selection issues as will the people with college algebra.

Your null is that algebra does not matter. The alternative is that it does. If the p-value is less than your cutoff, chosen before collecting the data, then you can reject the null. If it is not, then you should behave as if it is true until you either do more research or find another way to come to a conclusion.

It would be dubious, ignoring the methodology issues, to assert that college algebra matters as you only have one sample. The method is intended for repetition. Nonetheless, you would only be made a fool of no more than percent of the time, ignoring the methodological issues by following the results of the test.

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It appears you are asking for clarification..

A null, Ho, essentially predicts no effect (no difference between groups, no correlation/association between variables etc), whereas an alternative/experimental, Ha or H1 predicts an effect.

So in your example, you have the gist of Ho and Ha (though the wording could be improved).

Your Chi-square test gives you a chi-square value - you need to either a) compare this with a 'critical' chi-square value b) know the p-value associated with your chi-square value and compare this with an 'alpha' p-value (typically .05 in psychology for example)

These amount to the same kind of thing For this example, if your alpha/cutoff is .05, then your 'critical' chi-square is 3.841.

NHST requires that, if your p-value is LESS than your alpha/cutoff, then you reject the null.

Here's where the confusion might arise: As chi-square values increase, associated p values decrease.

So, if your chi-square value is SMALLER than the critical, your associated p-value would be LARGER than the alpha/cutoff. If p is larger, the null is NOT rejected.

If your chi-square value is LARGER than the critical, your associated p-value would be SMALLER than the alpha/cutoff. If p is smaller, the null IS rejected.

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Omniconvert
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Null and Alternative Hypothesis in A/B Testing
January 14, 2025 - To recap: the alternative hypothesis presents a contrasting idea to the null hypothesis. While the null hypothesis suggests a certain outcome is true, the alternative hypothesis proposes that the opposite is true.
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Laerd Statistics
statistics.laerd.com › statistical-guides › hypothesis-testing-3.php
Hypothesis Testing - Significance levels and rejecting or accepting the null hypothesis
The alternative hypothesis states the opposite and is usually the hypothesis you are trying to prove (e.g., the two different teaching methods did result in different exam performances). Initially, you can state these hypotheses in more general terms (e.g., using terms like "effect", ...
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ScienceDirect
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Alternative Hypothesis - an overview | ScienceDirect Topics
The hypothesis that we want to test is called a null hypothesis, while the opposite is called the alternative hypothesis. In the above coin-toss example, the null hypothesis is that the coin is not biased (i.e., the probability of obtaining heads is
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Lumen Learning
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Null and Alternative Hypotheses | Introduction to Statistics
The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality (=, ≤ or ≥) Always write the alternative hypothesis, typically denoted with Ha or H1, using less than, greater than, or not equals symbols, i.e., (≠, >, or <).
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Minitab
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About the null and alternative hypotheses - Minitab
The null and alternative hypotheses are two mutually exclusive statements about a population. A hypothesis test uses sample data to determine whether to reject the null hypothesis.
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Six Sigma Daily
sixsigmadaily.com › hypothesis (alternate/alternative)
Hypothesis (alternate/alternative) - Six Sigma Terminology
June 4, 2018 - The alternate hypothesis is the complement of the null hypothesis. The null hypothesis is what you anticipate through randomness. The alternative hypothesis, sometimes known as the alternate hypothesis is the opposite of that.
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Penn State Statistics
online.stat.psu.edu › stat502 › lesson › 1 › 1.2
1.2 - The 7 Step Process of Statistical Hypothesis Testing | STAT 502
The null hypothesis can be thought of as the opposite of the "guess" the researchers made. In the example presented in the previous section, the biologist "guesses" plant height will be different for the various fertilizers. So the null hypothesis would be that there will be no difference among ...
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University of West Georgia
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both what it is, how hypothesis tests are u
In general the null hypothesis states · that there is no change, no difference, no effect, and otherwise no relationship between · the independent and dependent variables. Because we are hypothesizing that nothing is ... The second hypothesis we state is the alternative hypothesis. The ...
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StatsDirect
statsdirect.com › help › basics › p_values.htm
P Values (Calculated Probability) and Hypothesis Testing - StatsDirect
The alternative hypothesis (H1) is the opposite of the null hypothesis; in plain language terms this is usually the hypothesis you set out to investigate.
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Chegg
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Null hypothesis | Chegg Writing
December 14, 2021 - But rather, the statement is something that needs to be nullified. The alternate hypothesis, which is often written as H1 or Ha, is the opposite of the null hypothesis. The alternate hypothesis is what researchers want to test when seeking to reject the null hypothesis.
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Statistics Solutions
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Null hypothesis and Alternative Hypothesis - Statistics Solutions
May 14, 2025 - The purpose is to test whether the hypothesis supports the research, independent of the investigator’s values and decisions. They also provide direction to the research. Researchers generally denote the null hypothesis as H0. It states the exact opposite of what an investigator or an experimenter predicts or expects.
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Numiqo
numiqo.com › tutorial › hypothesis
Hypothesis: A Beginner’s Guide
October 27, 2025 - A one-sided or directional alternative hypothesis includes only values that differ in one direction from the value of the null hypothesis.
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Formpl
formpl.us › blog › alternative-null-hypothesis
Alternative vs Null Hypothesis: Pros, Cons, Uses & Examples
November 22, 2021 - If you develop a null hypothesis, you make an informed guess on whether a thing is true or whether there is a relationship between that thing and another variable. An alternate hypothesis will always take an opposite stand against a null hypothesis.
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Study.com
study.com › skill › learn › how-to-write-an-alternative-hypothesis-for-a-given-situation-explanation.html
What is an Alternative Hypothesis For a Given Situation? | Statistics and Probability | Study.com
The opposite of greater than is "less than or equal to." Step 3: The alternative hypothesis is obtained by replacing the symbol in Step 1 with the symbol in Step 2 for the null hypothesis.