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# Suppose a researcher is testing someone to see if he or she can tell Soda X from Soda​ Y, and the researcher is using 28 ​trials, half with Soda X and half with Soda Y. The null hypothesis is that the person is guessing. The alternative is​ one-sided, Upper H Subscript a​: p 0greater than0.5. The person gets 17 right out of 28. The​ p-value comes out to be 0.129. Explain the meaning of the​ p-value.

Accepted Solution

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Answer:The probability that a person will get 17 or more​ right, if the person is truly​ guessing, is about 12.9%.The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct.Step-by-step explanation:The system of hypothesis fo this case are:Null hypothesis: $$p\leq 0.5$$Alternative hypothesis: $$p >0.5$$That's a upper right tailed test. The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct. And this value allows to reject or not the null hypothesis.If $$p_v <\alpha$$ we reject the null hypotheis at the significance level. That indicates strong evidence against the null hypothesis, so you reject the null hypothesis. If $$p_v>\alpha$$ then we say that we fail to reject the null hypothesis at the significance level. That indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.