Testing Claims about a Population Mean Objective: test a claim

 Student’s t-distribution with n-1 degrees of freedom  List properties:

1. Determine the null and alternative hypotheses 2. Select a level of significance 3. Compute the test statistic 4. Determine the critical value 5. Compare the critical value with the test statistic Reject the null hypothesis if the test statistic falls within the critical region!! 6. State the conclusion

Test the weight of Skittles as if you were a quality-control engineer. Because shutting down the plant is very expensive, test the claim at 0.01 level of significance.

The US Golf Association requires that golf balls have a diameter that is 1.68 inches. An engineer wishes to discover whether Maxfli XS golf balls have a mean diameter different from 1.68 inches. A random sample of Maxfli XS golf balls was selected

(1) State the null and alternative hypotheses H 0 : μ=1.68H 1 : μ≠1.68 (2) Select α α=0.05 (3) Find the t-score t0=t0= (4) Find the critical value (4) Determine p-value t 0.05/2 =±2.201 p= (5) Compare t-score (5) Compare p-value to critical value to α 0.77 < 2.201,so do not reject H < , so do not reject H 0 (6) State the conclusion There is not sufficient evidence to support the claim that the diameter of the golf balls does not equal 1.68.

 If using the calculator, you can have the calculator do a t-test, which will give the p- value. You compare it to the level of significance.  Reject the null hypothesis if the p-value < α.  Assignment: page 5381 – 8, 13, 15, 23