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## In statistics, we always assume the null hypothesis is true.

Type II error (False negative): The null hypothesis is not rejected when it is false.

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# Null and Alternative Hypotheses for a Mean

Note: In computing the Z-test statistic for a proportion we use the hypothesized value po here not the sample proportion p-hat in calculating the standard error! We do this because we "believe" the null hypothesis to be true until evidence says otherwise.

Having said that, there's one key concept from Bayesian statistics that is important for all users of statistics to understand. To illustrate it, imagine that you are testing extracts from 1000 different tropical plants, trying to find something that will kill beetle larvae. The reality (which you don't know) is that 500 of the extracts kill beetle larvae, and 500 don't. You do the 1000 experiments and do the 1000 frequentist statistical tests, and you use the traditional significance level of PPPP value, after all), so you have 25 false positives. So you end up with 525 plant extracts that gave you a P value less than 0.05. You'll have to do further experiments to figure out which are the 25 false positives and which are the 500 true positives, but that's not so bad, since you know that most of them will turn out to be true positives.

## the null hypothesis is rejected when it is true b.

Kleinbaum - Univ of North Carolina True/FalseTESTOFSIGNIFICAN CONCEPT STATISTICST= 2 ComprehensionD= 5 GeneralBack to 1657-1Back to 1657-2Back to 1657-3

Kleinbaum - Univ of North Carolina True/FalseTESTOFSIGNIFICAN SCOPEOFINFERENCE CONCEPT STATISTICST= 2 ComprehensionD= 5 GeneralBack to 1655-2Back to 1655-3

## the result would be unexpected if the null hypothesis were true c.

Mickey -UCLA True/FalseTYPE1ERROR TESTING CONCEPT STATISTICST= 2 ComprehensionD= 3 GeneralBack to 1489-1Back to 1490-1

Mickey -UCLA True/FalseBASICTERMS/STATS TYPE1ERROR STATISTICS CONCEPTT= 2 ComprehensionD= 2 GeneralBack to 1280-1Back to 1285-1

• ### failing to reject the null hypothesis when it is true.

The two competing statements about a population are called the null hypothesis and the alternative hypothesis.

• ### rejecting the null hypothesis when it is true.

the probability of Y falling in the critical region when the null hypothesis is true is ALPHA II.

• ### rejecting the null hypothesis when the alternative is true.

A Type I error is committed when one accepts the null hypothesis when it is false.

## not rejecting the null hypothesis when the alternative is true.

: The word isn't used much in everyday language, but when it is, it is often applied to ideas that have been shown to be untrue. When that's the case  when an idea has been shown to be false  a scientist would say that it has been falsified. A falsifi idea, on the other hand, is one for which there is a conceivable that might produce evidence proving the idea false. Scientists and others influenced by the ideas of the philosopher Karl Popper sometimes assert that only falsifiable ideas are scientific. However, we now recognize that science cannot once-and-for-all prove any idea to be false (or true for that matter). Furthermore, it's clear that evidence can play a role in supporting particular ideas over others  not just in ruling some ideas out, as implied by the falsifiability criterion. When a scientist says , he or she probably actually means something like , the term we use in this website to avoid confusion. A testable idea is one about which we could gather evidence to help determine whether or not the idea is accurate.

## the null hypothesis is rejected when it is true.

Alternative hypothesis – SCL will have a significance effect on how primary school students learn English skills compared to when they’re taught using a teacher-centered approach

## the result would be unexpected if the null hypothesis were true.

: In everyday language, generally refers to something that a fortune teller makes about the future. In science, the term generally means "what we would expect to happen or what we would expect to observe if this idea were accurate." Sometimes, these scientific predictions have nothing at all to do with the future. For example, scientists have hypothesized that a huge asteroid struck the Earth 4.5 billion years ago, flinging off debris that formed the moon. If this idea were true, we would that the moon today would have a similar composition to that of the Earth's crust 4.5 billion years ago  a prediction which does seem to be accurate. This hypothesis deals with the deep history of our solar system and yet it involves predictions  in the scientific sense of the word. Ironically, scientific predictions often have to do with past events. In this website, we've tried to reduce confusion by using the words and instead of and . To learn more, visit in our section on the core of science.

## The failure to reject does not imply the null hypothesis is true.

In the second experiment, you are going to put human volunteers with high blood pressure on a strict low-salt diet and see how much their blood pressure goes down. Everyone will be confined to a hospital for a month and fed either a normal diet, or the same foods with half as much salt. For this experiment, you wouldn't be very interested in the P value, as based on prior research in animals and humans, you are already quite certain that reducing salt intake will lower blood pressure; you're pretty sure that the null hypothesis that "Salt intake has no effect on blood pressure" is false. Instead, you are very interested to know how much the blood pressure goes down. Reducing salt intake in half is a big deal, and if it only reduces blood pressure by 1 mm Hg, the tiny gain in life expectancy wouldn't be worth a lifetime of bland food and obsessive label-reading. If it reduces blood pressure by 20 mm with a confidence interval of ±5 mm, it might be worth it. So you should estimate the effect size (the difference in blood pressure between the diets) and the confidence interval on the difference.

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