Question

Listed below are the number of homeruns for the National League leader over the last 20 years, through 2006. Assuming that number of homeruns is normally distributed, if this is sample data collected from a population of all past and future homerun leaders, test the claim that the mean homerun leader has less than 47 homeruns, where á=.05. Set up and complete the appropriate hypothesis test. For this data, also compute the p-value and describe how you could have used this information to complete the analysis. Finally, compute 85% and 98% Confidence Intervals for this data.
Year Homeruns Year Homeruns
2006 58 1996 47
2005 51 1995 40
2004 48 1994 43
2003 47 1993 46
2002 49 1992 35
2001 73 1991 38
2000 50 1990 40
1999 65 1989 47
1998 70 1988 39
1997 49 1987 49

Answer 1

Here's a few hints:

1. Set up a null and alternative hypothesis based on the information given.
2. The test will be a one-sample z-test (the number of homeruns is normally distributed). You will need to find mean and standard deviation of the data.
3. The p-value is the actual level of the test statistic (found using a z-table).
4. Use appropriate confidence formulas
for the data. (You will have to check a z-table again to determine z for each interval.)

I hope this will give you some clues on how to get started on this one.