M 384G/374G, Fall 04
Understanding hypothesis tests
A. Suppose we have used a simple random sample of size n from a certain
population to perform a t-test with null hypothesis
NH: E(y) = h
and alternate hypothesis
AH: E(y) > h.
Which of the following statements best expresses the assertion that
the p-value is .04? What is problematic about the rest?
1.The probability that E(y) = h is .04.
2. The probability of obtaining the test statistic calculated from our data
is 0.04, assuming we are taking simple random samples of the same size and
the null hypothesis is true.
3. The probability of obtaining a value of t at least as large as the one
we obtained from our sample is .04.
4. If it is true that E(y) = h, then the probability of obtaining a value
of t (from a sample taken from the population in question) at least
as large as the one we obtained from our sample is .04.
5. If it is true that E(y) = h, then the probability of obtaining a
value of t (from a simple random sample taken from the population in
question) at least as large as the one we obtained is .04.
6. If it is true that E(y) = h, then the probability of obtaining a
value of t (from a simple random sample of size n taken from the population
in question) at least as large as the one we obtained is .04.
B. Suppose we have performed a hypothesis test with null hypothesis
NH: E(y) = h
and alternate hypothesis
AH: E(y) ≠ h,
and that we have obtained the p-value. For each of the statements 1 - 5
below, decide which of the following best characterizes the statement: Accurate
statement, ambiguous (might be correct or incorrect depending on the interpretation),
needs more detail, definitely wrong, just gives the intuitive idea, reasonable
conclusion, nonsense.
1. If the p-value is .03, then there is a 3% chance that the null
hypothesis is wrong.
2. If we reject the null hypothesis at the significance level a, then the
probability that the null hypothesis is true equals a.
3. The p-value is the probability of observing a value of the test statistic
at least as extreme as the one we actually obtained.
4. The p-value is the probability of observing a value of the test statistic
at least as extreme as the one we actually obtained, if indeed the null hypothesis
is true, assuming that we are only taking simple random samples of the same
size from the same population.
5. The p-value is a measure of the weight of the evidence against the null
hypothesis, with small values providing evidence against the null hypothesis.