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.
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Relational Symbols | |||
---|---|---|---|
= | equals is the same as | ≠ | is not equal to is different from |
> | is greater than is more than exceeds is above | ≥ or >= | is greater than or equal to is at least is not less than |
< | is less than is fewer than is below | ≤ or <= | is less than or equal to is at most does not exceed is not greater than is no more than |
< < | is between and , exclusive | ||
≤ ≤ | is between and , inclusive | ||
≈ | is approximately equal to |
Here are symbols for various sample statistics and the corresponding population parameters. They are not repeated in the list below.
sample statistic | population parameter | description |
---|---|---|
number of members of sample or population | ||
“x-bar” | μ “mu” or μ | mean |
or Med or “x-tilde” | (none) | median |
(TIs say Sx) | σ “sigma” or σ | standard deviation For variance, apply a squared symbol ( ² or σ²). |
ρ “rho” | coefficient of linear correlation | |
“p-hat” | proportion | |
χ² | (n/a) | calculated test statistic |
μ and σ can take subscripts to show what you are taking the mean or standard deviation of. For instance, σ x̅ (“sigma sub x-bar”) is the standard deviation of sample means, or standard error of the mean.
In geometric and binomial probability distributions, p is the probability of “success” ( defined here in Chapter 6) on any one trial and q = (1− p ) is the probability of “failure” (the only other possibility) on any one trial.
In hypothesis testing, p is the calculated p-value ( defined here in Chapter 10), the probability that rejecting the null hypothesis would be a wrong decision.
In tests of population proportions, p stands for population proportion and p̂ for sample proportion (see table above).
Caution! The order of A and B may seem backward to you at first.
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Symbol | Format | Data |
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μ | ||
The Greek letter (mu) is used in statistics to represent the population mean of a distribution.
The x bar (x̄) symbol is used in statistics to represent the sample mean, or average, of a set of values. It's calculated by adding up all the numbers in the sample and then dividing by the number of values in that sample.
The Greek capital letter Μ is visually very similar to the Latin capital letter M. For that reason, refer to the usage of the Latin capital letter M for math usage.
The population mean formula gives the average value of the whole population.
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The actual test begins by considering two hypotheses. They are called the null hypothesis and the alternative hypothesis. These hypotheses contain oppos...
The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test: Null hypothesis
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.
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.
The null hypothesis is a hypothesis in which the sample observation results from chance. Learn the definition, principles, and types of the null hypothesis at BYJU'S.
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.
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 ).
The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test: Null hypothesis
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.
Basic definitions. 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 ...
The choice of symbol depends on the wording of the hypothesis test. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.
The null hypothesis in statistics states that there is no difference between groups or no relationship between variables. It is one of two mutually exclusive hypotheses about a population in a hypothesis test. When your sample contains sufficient evidence, you can reject the null and conclude that the effect is statistically significant.
Here are the differences between the null and alternative hypotheses and how to distinguish between them.
In hypothesis testing there are two mutually exclusive hypotheses; the Null Hypothesis (H0) and the Alternative Hypothesis (H1). One of these is the claim to be tested and based on the sampling results (which infers a similar measurement in the population), the claim will either be supported or not. The claim might be that the population ...
In order to sort out the difference between a chance effect and a statistically significant effect we start by writing a pair of statements called hypotheses: a null hypothesis and the alternative hypothesis. The hypotheses are statements made about what we believe to be true with regards to the population mean (represented by the Greek letter mu ( μ )).
The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis.
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 ≤).
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.
In hypothesis testing, p is the calculated p-value (defined here in Chapter 10), the probability that rejecting the null hypothesis would be a wrong decision. In tests of population proportions, p stands for population proportion and p̂ for sample proportion (see table above). P (A) = the probability of event A.
The Greek letter μ (mu) is used in statistics to represent the population mean of a distribution.