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Publishing scientific papers online is fast, and the papers can be long. Publishing in a paper journal means that the paper will live forever in libraries. The British Medical Journal combines the two; it prints short and reasonable versions, with longer versions available online. Is this OK with authors?
The journal asked about a random sample of 104 of its recent authors' several questions. One question was, "Should the journal continue using this system?"
In the sample, 72 said "yes."
(a) do the data give good evidence that more than two-thirds (67%) of authors support continuing this system? carry out an appropriate test to help answer this question.
(b) interpret the p-values from your test in the context of the problem.

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Answer:

There is no significant evidence that more than two-thirds (67%) of authors support continuing this system.

Step-by-step explanation:

Let p be the proportion of authors who support continuing the system

Then hypotheses are:

[tex]H_{0}[/tex]: p=0.67

[tex]H_{a}[/tex]: p>0.67

To calculate the test statistic:

z=[tex]\frac{p(s)-p}{\sqrt{\frac{p*(1-p)}{N} } }[/tex] where

  • p(s) is the sample proportion of authors who support the publishing system ([tex]\frac{72}{104} [/tex] ≈0.692)
  • p is the proportion assumed under null hypothesis. (0.67)
  • N is the sample size (104)

Then z=[tex]\frac{0.692-0.67}{\sqrt{\frac{0.67*0.33}{104} } }[/tex] ≈ 0.477

p-value of test statistic is ≈0.317

Assuming a significance level 0.05, since 0.317>0.05 we fail to reject the null hypothesis.

p-value 0.317 is the probability that the sample is drawn from the distribution assumed under null hypothesis, that is where the proportion of authors supporting the new publishing system is at most 0.67

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