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Chapter 10: Problem 23

Use the definition of the \(P\) -value to explain the following: a. Why \(H_{0}\) would be rejected if \(P\) -value \(=.0003\) b. Why \(H_{0}\) would not be rejected if \(P\) -value \(=.350\)

Short Answer

Expert verified
If the \(P\)-value is .0003, which is much less than .05, the null hypothesis (\(H_{0}\)) would be rejected. Conversely, if the \(P\)-value is .350, which is much more than .05, the null hypothesis (\(H_{0}\)) would not be rejected.

Step by step solution

01

Understand the \(P\)-value

The \(P\)-value is a statistical measure that helps scientists determine whether or not their hypotheses are correct. It is a calculated probability that's used in the hypothesis testing process. Usually, if the \(P\)-value of a data set is below a certain pre-determined amount (like .05 or 5%), scientists will reject the 'null hypothesis'(\(H_{0}\)), and accept the alternative hypothesis.
02

Determine why \(H_{0}\) would be rejected for \(P\)-value = .0003

In this case, the \(P\)-value is .0003. This is considerably less than .05 (which is the usual threshold at which one might reject the null hypothesis). Hence, if the obtained \(P\)-value is .0003, which is much smaller than .05, we reject the null hypothesis.
03

Determine why \(H_{0}\) would not be rejected for \(P\)-value = .350

In this case, the \(P\)-value is .350. This is much higher than the standard .05 threshold, meaning that the data you've obtained is much more likely to occur if your null hypothesis is correct. Hence, if the obtained \(P\)-value is .350, which is much greater than .05, we don't reject the null hypothesis.

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Most popular questions from this chapter

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