Question

1. if a studys p - value is 0.03, and the significance level is set at 0.05, what should be concluded?

a. increase the sample size and retest.
b. accept the null hypothesis.
c. the result is likely due to chance.
d. reject the null hypothesis.

Explanation:

In hypothesis testing, if the p - value ($p = 0.03$) is less than the significance level ($\alpha=0.05$), we reject the null hypothesis. Option a is about sample size adjustment which is not relevant here as the decision rule is based on $p$ and $\alpha$. Option b is incorrect because when $p<\alpha$ we do not accept the null. Option c is wrong as a small $p$ - value ($p = 0.03<0.05$) suggests the result is not likely due to chance.

Answer:

d. Reject the null hypothesis.