8.2 p value guided notes
- 1. AP/H Statistics Mrs. LeBlanc Perrone Name: ______________________________ 8.2: P-ValueGuided Notes Date: ___________ 8.2 TESTING THE MEAN (P VALUES) How to Test When is Known 1. ______________________________________________________________________________ o ________________________________________________________________________ o ________________________________________________________________________ o ________________________________________________________________________ ________________________________________________________________________ o ________________________________________________________________________ 2. ______________________________________________________________________________ ______________________________________________________________________________ 3. ______________________________________________________________________________ ______________________________________________________________________________ o 4. ______________________________________________________________________________ ______________________________________________________________________________ o ________________________________________________________________________ 5. ______________________________________________________________________________ o ________________________________________________________________________ o ________________________________________________________________________ 6. ______________________________________________________________________________ 1
- 2. AP/H Statistics Mrs. LeBlanc Perrone EXAMPLE 3: Testing , known Sunspots have been observed for many centuries. Records of sunspots from ancient Persian and Chinese astronomers go back thousands of years. Some archaeologists think sunspot activity may somehow be related to prolonged periods of drought in the southwestern United States. Let be a random variable representing the average number of sunspots observed in a four-week period. A random sample of 40 such periods from Spanish colonial times gave the following data (Reference: M. Waldmeir, Sun Spot Activity, International Astronomical Union Bulletin). The sample mean is Previous studies of sunspot activity during this period indicate that . It is thought that for thousands of years, the mean number of sunspots per four-week period was about = 41. Sunspot activity above this level may (or may not) be linked to gradual climate change. Do the data indicate that the mean sunspot activity during the Spanish colonial period was higher than 41? Use = 0.05. 2
- 3. AP/H Statistics Mrs. LeBlanc Perrone How to Test When is Unknown 1. ______________________________________________________________________________ o ________________________________________________________________________ o ________________________________________________________________________ o ________________________________________________________________________ ________________________________________________________________________ o ________________________________________________________________________ 2. ______________________________________________________________________________ ______________________________________________________________________________ 3. ______________________________________________________________________________ ______________________________________________________________________________ o 4. ______________________________________________________________________________ ______________________________________________________________________________ o ________________________________________________________________________ 5. ______________________________________________________________________________ o ________________________________________________________________________ o ________________________________________________________________________ 6. ______________________________________________________________________________ Calculating the P-Value for Testing When is Unknown 1. Hit STAT, Tab over to TESTS, Choose option 2: T Test 2. Highlight STATS and Hit ENTER 3. Enter the information, highlight the alternate hypothesis, highlight Calculate and hit ENTER o : from o o o 4. Enter the information, highlight the alternate hypothesis, highlight Calculate and hit ENTER o : from o o o 5. Your screen will give you the P-value 3
- 4. AP/H Statistics Mrs. LeBlanc Perrone EXAMPLE 4: Testing , unknown The drug 6-mP (6-mercaptopurine) is used to treat leukemia. The following data represent the remission times (in weeks) for a random sample of 21 patients using 6-mP (Reference: E. A. Gehan, University of Texas Cancer Center). The sample mean is 17.1 weeks, with sample standard deviation s 10.0. Let be a random variable representing the remission time (in weeks) for all patients using 6-mP. Assume the distribution is mound-shaped and symmetric. A previously used drug treatment had a mean remission time of = 12.5 weeks. Do the data indicate that the mean remission time using the drug 6- mP is different (either way) from 12.5 weeks? Use = 0.01. 4
- 5. AP/H Statistics Mrs. LeBlanc Perrone Summary Questions 1. What are the requirements for normality when in known? What are the requirements for normality when in unknown? ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 2. Generalize the procedure for calculating the sample test statistic for the mean. What are the similarities? What are the differences? ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 3. Consider a test for . If the P-value is such that you can reject at the 5% level of significance, can you always reject at the 1% level of significance? Explain. ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 4. Consider a test for . If the P-value is such that you can reject at the 1% level of significance, can you always reject at the 5% level of significance? Explain. ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ HOT Question: __________________________________________________________________________________________ __________________________________________________________________________________________ 5