A p-value of a one-sided hypothesis test is 0.035. At the 5% significance level, what would be the correct conclusion if the hypothesis was two-sided?
Question
A p-value of a one-sided hypothesis test is 0.035. At the 5% significance level, what would be the correct conclusion if the hypothesis was two-sided?
Solution
In a two-sided hypothesis test, the p-value needs to be divided by 2 to compare with the significance level. This is because a two-sided test accounts for the possibility of the observed effect being in either direction.
So, if we have a p-value of 0.035 in a one-sided test, it would be 0.035/2 = 0.0175 in a two-sided test.
The significance level is 0.05 (5%).
Since the p-value (0.0175) is less than the significance level (0.05), we would reject the null hypothesis. This means there is sufficient evidence to suggest that the alternative hypothesis is true at the 5% significance level.
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