Question

For a given hypothesis test, the p-value of the test statistic equals 0.032. This implies a 0.032 probability of making a:

a.) Type I error
b.) Type II error
c.) Correct rejection of the null
d.) Correct acceptance of the null

Answer 1

Given that p-value is 0.0.32. Since the definition of p-value is "In statistics , the p-value is the probability of obtaining results as extreme as the observed results of a statistical hypothesis test,assuming that the null hypothesis is correct." The p-value is not equal to probability of type -1 error always.For one tailed test p-value is the probability that the random variable is greater than test statistic if test statistic is positive( for negative test statistics we calculate the probability that random is less than test statistic).For two tailed test p-value = 2×p-value of one tailed test.

So according to the above explanation it is not a type-1 error because type -1 error is the probability of rejecting null hypothesis means it only give the reject region but p-value may lie in acceptance or rejection region.If p-value lies in rejection region then for probability that random variable greater than test statistics will be less than type one error and for negative random variable less than test statistics is less than type one error.So option a) is incorrect, and type-2 error is the probability of accepting alternative hypothesis when alternative hypothesis is wrong so option b) is incorrect ,since according to the explanation of p-value that p-value give the correct rejection for null hypothesis so option d) is wrong so option c) is the right answer.