Chapter 9: Hypothesis Tests for One Population Mean 9.5 P-Values

P-Value To obtain: – Assume the null hypothesis is true – Compute the probability of observing a value of the test statistic as extreme or more extreme than that observed

If z 0 is the observed value of the test statistic… Obtain the P-value as follows: Two-tailed test: use the sum of both tails of the graph (area under curve) Left-tailed/right-tailed: use the area under the curve for the tail

Example 9.12 Consider again the history book hypothesis test of Example 9.7 where we wanted to decide whether this year’s mean cost of all history books has increased from the 1997 mean of $ Recall that the null and alternative hypotheses are: Table 9.5 (p. 405) displays this year’s prices for 40 randomly selected history books, for which the mean price is $ Using that sample mean and σ = $7.61, we found the value of the test statistic to be Obtain and interpret the P-value of the hypothesis test.

Key Facts The P-value of a hypothesis test equals the smallest significance level at which the null hypothesis can be rejected. If the P-value is less than or equal to the specified significance level, reject the null hypothesis; otherwise, do not reject the null hypothesis.

The One-Sample z-Test for a Population Mean (P-value approach) Assumptions: – Normal populations – σ known Step 1: decide on the null and alternative hypothesis Step 2: decide on the significance level, α Step 3: compute the value of the test statistic Step 4: use table II to obtain the P-value Step 5: if P ≤ α, reject null Step 6: interpret results

Homework P – 80