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Samples, Populations, and Inferential Statistics

Researchers rarely study entire .
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Instead, their findings are based on data.
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statistics are used to determine whether we can infer that the results reflect what would happen if the study was conducted again and again with multiple samples.
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Thus, we are asking whether we can infer that the results from a are reflective of the true results for the population.
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Hypotheses and Probability

Statistical inference begins with a statement of the null hypothesis and the hypothesis.
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The hypothesis is a very precise statement that the population means are .
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On the other hand, the hypothesis is that the population means are equal.
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The research hypothesis cannot be as as the null hypothesis, so we infer that the research hypothesis is correct only by the null hypothesis.
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The hypothesis is rejected only when there is a very low probability that the obtained results could be due to random .
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This is what is meant by statistical .
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is the likelihood some event or outcome will happen. It is used in statistical inference much the same way.
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If the probability of obtaining the result because of random error is very low, we the possibility that only random or chance error is responsible for the obtained difference in the means.
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Sampling Distributions

Outcome probabilities are derived from a probability distribution called distributions.
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Likewise, all statistical are based on probability distributions that are referred to as distributions.
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The sampling distribution is based on the assumption that the is true.
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When the obtained results are highly unlikely, you conclude that you have not sampled from the distribution specified by the null hypothesis.
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Usually, if this probability is less than , the researcher decides to reject the null hypothesis and the research hypothesis.
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Type I and Type II Errors

When we reject the null hypothesis but the null hypothesis is actually true, a error is made.
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Type I errors occur when, simply by , we obtain a large value on a statistical test.
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The probability of making a Type I error is determined by the choice of significance or level.
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When the alpha level is .05 and the null hypothesis is rejected, it means that there are 5 chances out of that the decision is wrong.
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A error occurs when the null hypothesis is accepted and the research hypothesis is true.
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The means are not equal, but the results of the experiment do not lead to a decision to the null hypothesis.
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Researchers generally believe that the consequences of making a error are more serious than those associated with a Type II error.
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If the hypothesis is rejected, the researcher might publish the results in a journal, and the results might be reported to others in textbooks, newspapers, or magazines.
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Since researchers do not want to mislead people, they guard against the possibility of a Type I error by using a very significance level.
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The Importance of Replications

It is important to note that scientists do not attach too much importance to the results of a study.
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Instead, scientists are more confident in the findings when the study is .







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