Question

the p - value for a hypothesis test turns out to be 0.09871. at a 10% level of significance, what is the proper decision?
o we have sufficient evidence for our alternative hypothesis, thus we will reject ho
o we have insufficient evidence for our alternative hypothesis, thus we will fail to reject ho
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Explanation:

Step1: Recall p - value decision rule

The decision rule for a hypothesis test using the p - value is: If the p - value is less than or equal to the significance level ($\alpha$), we reject the null hypothesis ($H_0$); if the p - value is greater than the significance level, we fail to reject the null hypothesis.
Here, the significance level $\alpha = 10\%=0.10$ and the p - value $= 0.09871$.

Step2: Compare p - value and $\alpha$

We compare $0.09871$ and $0.10$. Since $0.09871<0.10$ (the p - value is less than the significance level), we have sufficient evidence to support the alternative hypothesis and we reject the null hypothesis $H_0$.

Answer:

We have sufficient evidence for our alternative hypothesis, thus we will reject \( H_0 \)