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Chapter 8: Problem 61

When comparing two sample proportions with a two-sided alternative hypothesis, all other factors being equal, will you get a smaller p-value if the sample proportions are close together or if they are far apart? Explain.

Short Answer

Expert verified
When comparing two sample proportions with a two-sided alternative hypothesis, the p-value will be smaller if the sample proportions are far apart. This is because far-apart proportions indicate that the observable difference is less likely due to chance.

Step by step solution

01

Understanding p-value

The p-value is a crucial measurement in hypothesis testing. If it is small (typically 鈮� 0.05), the null hypothesis is rejected in favor of the alternative hypothesis. Conversely, a larger p-value suggests that changes in your observations are likely due to chance and not due to the variables you're measuring.
02

Evaluating p-value in two sample proportion test.

In a two-sample proportion test, the p-value helps understand whether the difference in the proportion of successes in two groups could have happened by chance. If the sample proportions are close to each other, then the differences observed could more likely be due to random chance, hence a larger p-value. On the other hand, if the sample proportions are far apart, it is less likely that the difference is due to chance, hence a smaller p-value.
03

Conclusion

Therefore, when comparing two sample proportions with a two-sided alternative hypothesis, all other factors being equal, one would get a smaller p-value if the sample proportions are far apart. This is because when sample proportions are far apart, it signifies that the difference between the groups is less likely to be due to chance, thereby leading to a smaller p-value.

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