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Five Steps in a Hypothesis Test

CORRECTION: When newspapers make statements like, "most scientists agree that human activity is the culprit behind global warming," it's easy to imagine that scientists hold an annual caucus and vote for their favorite hypotheses. But of course, that's not quite how it works. Scientific ideas are judged not by their popularity, but on the basis of the evidence supporting or contradicting them. A hypothesis or theory comes to be accepted by many scientists (usually over the course of several years — or decades!) once it has garnered many lines of supporting evidence and has stood up to the scrutiny of the scientific community. A hypothesis accepted by "most scientists," may not be "liked" or have positive repercussions, but it is one that science has judged likely to be accurate based on the evidence. To learn more about , visit our series of pages on the topic in our section on how science works.

CORRECTION: This misconception likely stems from introductory science labs, with their emphasis on getting the "right" answer and with congratulations handed out for having the "correct" hypothesis all along. In fact, science gains as much from figuring out which hypotheses are likely to be wrong as it does from figuring out which are supported by the evidence. Scientists may have personal favorite hypotheses, but they strive to consider multiple hypotheses and be unbiased when evaluating them against the evidence. A scientist who finds evidence contradicting a favorite hypothesis may be surprised and probably disappointed, but can rest easy knowing that he or she has made a valuable contribution to science.

Hypothesis statement--a prediction that can be tested or an educated guess.

Hypothesis: Bacterial growth may be affected by temperature.

Hypothesis: Chocolate may cause pimples

A statistical hypothesis test is a procedure for deciding between two possible statements about a population. The phrase significance test means the same thing as the phrase "hypothesis test."

Last week we covered hypothesis tests for possible value of a population proportion (denoted by p). With some adjustments to the details of formulas we can use the same basic steps to carry out hypothesis tests for possible values of a population mean (denoted by the symbol μ).

A better way to write a hypotheses is to use a formalized hypotheses

We usually summarize a quantitative variable by examining the mean value. We summarize categorical variables by considering the proportion (or percent) in each category. Thus we use the methods described in this handout when the response variable is quantitative. Again, examples of quantitative variables are height, weight, blood pressure, pulse rate, and so on.

Null hypothesis: μ = 72  Alternative hypothesis: μ ≠72

: In everyday language, the word usually refers to an educated guess — or an idea that we are quite uncertain about. Scientific hypotheses, however, are much more informed than any guess and are usually based on prior experience, scientific background knowledge, preliminary observations, and logic. In addition, hypotheses are often supported by many different lines of evidence — in which case, scientists are more confident in them than they would be in any mere "guess." To further complicate matters, science textbooks frequently misuse the term in a slightly different way. They may ask students to make a about the outcome of an experiment (e.g., table salt will dissolve in water more quickly than rock salt will). This is simply a prediction or a guess (even if a well-informed one) about the outcome of an experiment. Scientific hypotheses, on the other hand, have explanatory power — they are explanations for phenomena. The idea that table salt dissolves faster than rock salt is not very hypothesis-like because it is not very explanatory. A more scientific (i.e., more explanatory) hypothesis might be "The amount of surface area a substance has affects how quickly it can dissolve. More surface area means a faster rate of dissolution." This hypothesis has some explanatory power — it gives us an idea of a particular phenomenon occurs — and it is testable because it generates expectations about what we should observe in different situations. If the hypothesis is accurate, then we'd expect that, for example, sugar processed to a powder should dissolve more quickly than granular sugar. Students could examine rates of dissolution of many different substances in powdered, granular, and pellet form to further test the idea. The statement "Table salt will dissolve in water more quickly than rock salt" is not a hypothesis, but an expectation generated by a hypothesis. Textbooks and science labs can lead to confusions about the difference between a hypothesis and an expectation regarding the outcome of a scientific test. To learn more about scientific hypotheses, visit in our section on how science works.

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Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

To determine it's truth value, first we look at thehypothesis: $x0$.

Fact: are statements that we know to be true through direct . In everyday usage, facts are a highly valued form of knowledge because we can be so confident in them. Scientific thinking, however, recognizes that, though facts are important, we can only be completely confident about relatively simple statements. For example, it may be a fact that there are three trees in your backyard. However, our knowledge of how all trees are related to one another is not a fact; it is a complex body of knowledge based on many different and reasoning that may change as new is discovered and as old evidence is interpreted in new ways. Though our knowledge of tree relationships is not a fact, it is broadly applicable, useful in many situations, and synthesizes many individual facts into a broader framework. values facts but recognizes that many forms of knowledge are more powerful than simple facts.

To determine it's truth value, first we look at thehypothesis: $01$.

: In everyday language, a is a rule that must be abided or something that can be relied upon to occur in a particular situation. Scientific laws, on the other hand, are less rigid. They may have exceptions, and, like other scientific knowledge, may be modified or rejected based on new evidence and perspectives. In science, the term usually refers to a generalization about and is a compact way of describing what we'd expect to happen in a particular situation. Some laws are non-mechanistic statements about the relationship among observable phenomena. For example, the ideal gas law describes how the pressure, volume, and temperature of a particular amount of gas are related to one another. It does not describe how gases behave; we know that gases do not precisely conform to the ideal gas law. Other laws deal with phenomena that are not directly observable. For example, the second law of thermodynamics deals with entropy, which is not directly observable in the same way that volume and pressure are. Still other laws offer more mechanistic explanations of phenomena. For example, Mendel's first law offers a of how genes are distributed to gametes and offspring that helps us make about the outcomes of genetic crosses. The term may be used to describe many different forms of scientific knowledge, and whether or not a particular idea is called a law has much to do with its discipline and the time period in which it was first developed.

For example: "I left asaucer of milk outside overnight.

CORRECTION: Scientists do strive to be unbiased as they consider different scientific ideas, but scientists are people too. They have different personal beliefs and goals — and may favor different hypotheses for different reasons. Individual scientists may not be completely objective, but science can overcome this hurdle through the action of the scientific community, which scrutinizes scientific work and helps balance biases. To learn more, visit in our section on the social side of science.

the null hypothesis is not rejected when it is false c.

For example, "Famous physicist John Taylor studied extensively and found noevidence of trickery or fraud in his feats." Taylor was notqualified to detect trickery or fraud of the kind used by stagemagicians.

the research hypothesis is rejected when it is true d.

CORRECTION: Perhaps because the last step of the Scientific Method is usually "draw a conclusion," it's easy to imagine that studies that don't reach a clear conclusion must not be scientific or important. In fact, scientific studies don't reach "firm" conclusions. Scientific articles usually end with a discussion of the limitations of the tests performed and the alternative hypotheses that might account for the phenomenon. That's the nature of scientific knowledge — it's inherently tentative and could be overturned if new evidence, new interpretations, or a better explanation come along. In science, studies that carefully analyze the strengths and weaknesses of the test performed and of the different alternative explanations are particularly valuable since they encourage others to more thoroughly scrutinize the ideas and evidence and to develop new ways to test the ideas. To learn more about publishing and scrutiny in science, visit our discussion of .

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