greater than (>) less than (<)
H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.
H 0 : No more than 30% of the registered voters in Santa Clara County voted in the primary election. p ≤ 30
H a : More than 30% of the registered voters in Santa Clara County 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 hypotheses.
H 0 : The drug reduces cholesterol by 25%. p = 0.25
H a : The drug does not reduce cholesterol by 25%. p ≠ 0.25
We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:
H 0 : μ = 2.0
H a : μ ≠ 2.0
We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : μ __ 66 H a : μ __ 66
We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:
H 0 : μ ≥ 5
H a : μ < 5
We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : μ __ 45 H a : μ __ 45
In an issue of U.S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.
H 0 : p ≤ 0.066
H a : p > 0.066
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. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : p __ 0.40 H a : p __ 0.40
In a hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis , typically denoted with H 0 . 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 H a or H 1 , using less than, greater than, or not equals symbols, i.e., (≠, >, or <). If we reject 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.
H 0 and H a are contradictory.
A sulfur copolymer with a pyrrole compound for the crosslinking of unsaturated elastomers †.
* Corresponding authors
a Politecnico di Milano, Department of Chemistry, Materials and Chemical Engineering “G. Natta”, Via Mancinelli 7, 20131 Milano, Italy E-mail: [email protected] , [email protected] , [email protected]
Effective applications must be found for sulfur, a widely available and inexpensive element. Over the last decade, copolymers with unsaturated comonomers have been prepared via so-called inverse vulcanization. In this work, a sulfur copolymer with a circular and biosourced di-pyrrole compound was obtained for the first time and was used as the sole crosslinking agent of an unsaturated elastomer. Pyrrole compounds (PyCs) were synthesized via the Paal–Knorr reaction of 2,5-hexanedione (HD) and hexamethylenediamine (HMD) or ethylenediamine (EDM). The PyCs were obtained without using solvents or catalysts in high yield and with water as the only co-product. Poly(S- co -HMDP) and poly(S- co -EDP) copolymers were prepared under the typical conditions of inverse vulcanization. Throughout the entire synthetic pathway, the overall yield was up to 92% and the atom efficiency was up to 73%. The E -factor evaluated for organic compounds was almost null. The sulfur weight content in the copolymers ranged from 40% to 80% and the average number of sulfur atoms in the sequences ranged from 3 to 17. The copolymers were found to be amorphous with a glass transition temperature ranging from −2 to 38 °C, increasing with the content of the pyrrole ring. The number average molecular weight was found to be in the range from 1500 to 9000 g mol −1 . The molecular weight distribution was pretty narrow, with values lower than 2. NMR investigation suggested that the β position of the pyrrole ring reacted with sulfur atoms. A poly(S- co -HMDP) copolymer with an average sequence of 3 sulfur atoms was used as the sole crosslinking agent in a composite based on an unsaturated elastomer such as poly(styrene- co -butadiene) from anionic polymerization. More efficient crosslinking was obtained by promoting the ionic reaction of sulfur with elastomer chains by using 1,5-diazabicyclo(5.4.0)undec-7-ene. These results pave the way for the synthesis of a wide variety of sulfur copolymers with comonomers containing pyrrole rings for the sustainable crosslinking of elastomers, avoiding the use of oil-based accelerators.
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S. Naddeo, V. Barbera and M. Galimberti, Polym. Chem. , 2024, Advance Article , DOI: 10.1039/D4PY00706A
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H 0 (Null Hypothesis): Population parameter =, ≤, ≥ some value. H A (Alternative Hypothesis): Population parameter <, >, ≠ some value. Note that the null hypothesis always contains the equal sign. We interpret the hypotheses as follows: Null hypothesis: The sample data provides no evidence to support some claim being made by an individual.
To distinguish it from other hypotheses, the null hypothesis is written as H 0 (which is read as "H-nought," "H-null," or "H-zero"). A significance test is used to determine the likelihood that the results supporting the null hypothesis are not due to chance. A confidence level of 95% or 99% is common. Keep in mind, even if the confidence level is high, there is still a small chance the ...
Revised on June 22, 2023. The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test: Null hypothesis (H0): There's no effect in the population. Alternative hypothesis (Ha or H1): There's an effect in the population. The effect is usually the effect of the ...
When your sample contains sufficient evidence, you can reject the null and conclude that the effect is statistically significant. Statisticians often denote the null hypothesis as H 0 or H A.. Null Hypothesis H 0: No effect exists in the population.; Alternative Hypothesis H A: The effect exists in the population.; In every study or experiment, researchers assess an effect or relationship.
An example of the null hypothesis is that light color has no effect on plant growth. The null hypothesis (H 0) is the hypothesis that states there is no statistical difference between two sample sets. In other words, it assumes the independent variable does not have an effect on the dependent variable in a scientific experiment.
Write a research null hypothesis as a statement that the studied variables have no relationship to each other, or that there's no difference between 2 groups. Write a statistical null hypothesis as a mathematical equation, such as. μ 1 = μ 2 {\displaystyle \mu _ {1}=\mu _ {2}} if you're comparing group means.
Null Hypothesis Examples. "Hyperactivity is unrelated to eating sugar " is an example of a null hypothesis. If the hypothesis is tested and found to be false, using statistics, then a connection between hyperactivity and sugar ingestion may be indicated. A significance test is the most common statistical test used to establish confidence in a ...
Step 1: Figure out the hypothesis from the problem. The hypothesis is usually hidden in a word problem, and is sometimes a statement of what you expect to happen in the experiment. The hypothesis in the above question is "I expect the average recovery period to be greater than 8.2 weeks.". Step 2: Convert the hypothesis to math.
10.1 - Setting the Hypotheses: Examples. A significance test examines whether the null hypothesis provides a plausible explanation of the data. The null hypothesis itself does not involve the data. It is a statement about a parameter (a numerical characteristic of the population). These population values might be proportions or means or ...
Here, the hypothesis test formulas are given below for reference. The formula for the null hypothesis is: H 0 : p = p 0. The formula for the alternative hypothesis is: H a = p >p 0, < p 0 ≠ p 0. The formula for the test static is: Remember that, p 0 is the null hypothesis and p - hat is the sample proportion.
The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test: Null hypothesis (H0): There's no effect in the population. Alternative hypothesis (HA): There's an effect in the population. The effect is usually the effect of the independent variable on the dependent ...
When your p-value is less than or equal to your significance level, you reject the null hypothesis. In other words, smaller p-values are taken as stronger evidence against the null hypothesis. Conversely, when the p-value is greater than your significance level, you fail to reject the null hypothesis. In this case, the sample data provides ...
Below are the primary purposes of the null hypothesis: 1. Baseline for Comparison. The null hypothesis provides a baseline or a default position that indicates no effect, no difference, or no relationship between variables. It is the statement that researchers aim to test against an alternative hypothesis.
The actual test begins by considering two hypotheses.They are called the null hypothesis and the alternative hypothesis.These hypotheses contain opposing viewpoints. \(H_0\): The null hypothesis: It is a statement of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.
The null hypothesis and the alternative hypothesis are types of conjectures used in statistical tests to make statistical inferences, which are formal methods of reaching conclusions and separating scientific claims from statistical noise.. 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 ...
When stating the null hypothesis, statisticians must identify all outcomes. For example, after examining a problem and identifying questions to ask, statisticians conclude that the null hypothesis is the expected outcome. ... Null hypothesis example Here is an example of how you can use a null hypothesis: State the null hypothesis
5.2 - Writing Hypotheses. The first step in conducting a hypothesis test is to write the hypothesis statements that are going to be tested. For each test you will have a null hypothesis ( H 0) and an alternative hypothesis ( H a ). Null Hypothesis. The statement that there is not a difference in the population (s), denoted as H 0.
The actual test begins by considering two hypotheses.They are called the null hypothesis and the alternative hypothesis.These hypotheses contain opposing viewpoints. H 0, the —null hypothesis: 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.
5. Phrase your hypothesis in three ways. To identify the variables, you can write a simple prediction in if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable. If a first-year student starts attending more lectures, then their exam scores will improve.
To test this, he can perform a one-tailed hypothesis test with the following null and alternative hypotheses: H 0 (Null Hypothesis): μ = 20 grams; H A (Alternative Hypothesis): μ ≠ 20 grams; This is an example of a two-tailed hypothesis test because the alternative hypothesis contains the not equal "≠" sign. The engineer believes that ...
The actual test begins by considering two hypotheses.They are called the null hypothesis and the alternative hypothesis.These hypotheses contain opposing viewpoints. H 0: The null hypothesis: It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.
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The E-factor evaluated for organic compounds was almost null. The sulfur weight content in the copolymers ranged from 40% to 80% and the average number of sulfur atoms in the sequences ranged from 3 to 17. The copolymers were found to be amorphous with a glass transition temperature ranging from −2 to 38 °C, increasing with the content of ...