the p-value for a significance test is .0358. a correct interpretation of this p-value would be:
a) about 3.6% of the data are significant
b) about 3.6% of all samples are significant
c) about 3.6% of all samples would produce a test statistic at least as extreme as ours if the null hypothesis is true
d) there is sufficient evidence to fail to reject the null hypothesis
The P value is the probability that the results you have found would occur solely by chance.
This should lead you to your answer. Thanks for asking.
The correct interpretation of the p-value depends on the significance level chosen for the test. The p-value represents the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, assuming the null hypothesis is true.
To interpret the p-value correctly, you need to compare it to the chosen significance level (typically denoted as α). If the p-value is less than or equal to α, then we have sufficient evidence to reject the null hypothesis. If the p-value is greater than α, then we do not have sufficient evidence to reject the null hypothesis.
Given that the p-value is 0.0358, the correct interpretation would be:
c) about 3.6% of all samples would produce a test statistic at least as extreme as ours if the null hypothesis is true
This interpretation is based on the assumption that a typically chosen significance level (α) is 0.05. If α = 0.05, then 0.0358 is less than 0.05, indicating that there is sufficient evidence to reject the null hypothesis.