1. CHAPTER 10 DAY 3

2. Warm-Up  Chapter 10 Packet #18-19  #18  μ = the diameter of a spindle (mm)  H 0 : μ = 5  H a : μ ≠ 5  #19  μ = mean household income  H 0 : μ = 42500  H a : μ > 42500

3. P-Value  The probability, computed assuming H 0 is true, that the test statistic would take a value as extreme or more extreme than the actually observed is called the P-value of the test.  We found the P-value using z-scores

4. Significance Level  The fixed value we compare the P-value with that we regard as decisive.  This is announced in advance as to how much evidence against H 0 we will insist on.  We use the Greek letter “alpha” or α for notation for the significance level. If no level of significance is given, assume that α =.05

5. Decision Rule Based on P-value  To use a P-value to make a conclusion in a hypothesis test, compare the P-value with α.  1. If P < α, then reject H 0  2. If P > α, then fail to reject H 0

6. Conclusion  Always state the conclusion in the context of the problem! Write a sentence to explain why you are rejecting or failing to reject H 0.

7. Hypothesis Testing Steps…  1. Define the variable. Identify H 0 and H a.  2. Find the z-score.  3. Find the P-value.  4. Decide whether or not to reject or fail to reject the null hypothesis.  5. Interpret the decision in the context of the original claim.

8. Example 1  Subway claims to sell a 12 inch sub ( σ = 0.25). You feel that the subs are actually shorter. Upon testing 5 subs, you find the mean to be 11.75 inches. At α =.01 is there enough evidence to support Subway’s claim?

9. Example 2  The U.S. Department of Agriculture reports that the mean cost of raising a child from birth to age 2 in a rural area is $9405 with a standard deviation of $1540. You believe this value is incorrect, so you select a random sample of 900 children (age 2) and find the mean cost is $9290. At α = 0.05, is there enough evidence to conclude that the mean cost is different from $9405?