A two-tailed test is conducted at the 5% significance level. What is the P-value required to reject the null hypothesis?
Answer: p<5%. You need the test statistic to find the p-value. If you get a p-value that is less than the level of significance of 0.05, then that will tell you to reject the null hypothesis.
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To find the P-value in a hypothesis test, you need to follow these steps:
1. Determine the null hypothesis (H0) and alternative hypothesis (Ha).
2. Choose an appropriate statistical test and calculate the test statistic.
3. Determine the significance level, which is the maximum P-value that allows us to reject the null hypothesis.
4. Calculate the P-value using the test statistic and the appropriate distribution.
5. Compare the P-value to the significance level to make a decision.
In this case, you mention a two-tailed test conducted at the 5% significance level. This means the significance level is 0.05, which is commonly denoted as α = 0.05. The 5% significance level is often used as a standard for hypothesis testing.
To reject the null hypothesis, the P-value needs to be less than the significance level (0.05 in this case). The P-value represents the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true.
So, if you obtain a P-value less than 0.05 (p < 0.05), that means the observed test statistic is highly unlikely to have occurred by chance under the assumption of the null hypothesis. Therefore, you would reject the null hypothesis in favor of the alternative hypothesis.
Remember that the P-value is not a direct probability of the null hypothesis being true or false. It simply helps us make a decision about the null hypothesis based on the observed data and the chosen significance level.