Choosing Significance Level

Section 10.3

Starter 10.3.1

At the local bakery, loaves of bread are supposed to weigh 1 pound, with standard deviation 0.13 pounds. You believe that today’s loaves are too heavy. You want to test this idea at the α = .05 level. You weigh 20 loaves and find a mean weight of 1.05 pounds.

1. State your null and alternative hypotheses.

2. Find the test statistic (z) and the p-value for your test by two different methods.

3. State your conclusion clearly in a complete sentence.

Today’s Objectives• Students should be able to discuss issues

involved with selecting the α level of a test

• Students should be able to state shortcomings of P-level as sole criterion– How do outliers affect P?– Why might a confidence interval be more

useful than a hypothesis test?

California Standard 18.0

Students determine the P- value for a statistic for a simple random sample from a normal distribution.

Choose an appropriate level of significance (alpha)

• How will the conclusion be used?

• How plausible is Ho

• What are the consequences of rejecting Ho?

• Assume SATM scores are N(475,100). 100 students take a prep course that claims to improve scores.

• State the null and alternative hypotheses.• If the students mean score is 491.4, is the

result significant at the 5% level?– Use the calculator Z-Test screen.

• If the mean is 491.5, is the result significant at the 5% level?

• Conclusion: There is nothing “magic” about 5%; don’t act as if it were!

There is more to statistical significance than P-value!

• Plot your data– Look for outliers– Is the effect you seek visible in the data?

• Use a confidence interval– Estimates the size of an effect, not just

presence or absence of the effect

Today’s Objectives• Students should be able to discuss issues

involved with selecting the α level of a test

• Students should be able to state shortcomings of P-level as sole criterion– How do outliers affect P?– Why might a confidence interval be more

useful than a hypothesis test?

California Standard 18.0

Students determine the P- value for a statistic for a simple random sample from a normal distribution.

Homework

• Read pages 560-566

• Do problems 61-65