Hypothesis Testing/P-Value

#1
My last question!

Listed below are the # of homeruns for the National League leader over the last 20 years. Assuming that # of homeruns is normally distributed, if this is sample data collected from a population of all past & future homerun leaders, test the claim that the mean homerun leader has less than 47 homeruns, where α=.05. Set up & complete the appropriate hypothesis test. For this data, also compute the p-value. Finally, compute 85% & 98% Confidence Intervals for this data.

Year (Homerun)
2006 (58)
2005 (51)
2004 (48)
2003 (47)
2002 (49)
2001 (73)
2000 (50)
1999 (65)
1998 (70)
1997 (49)
1996 (47)
1995 (40)
1994 (43)
1993 (46)
1992 (35)
1991 (38)
1990 (40)
1989 (47)
1988 (39)
1987 (49)

(The sum of all the homeruns is 984. The mean is 49.2)

I know this should be a left-tailed test since it states "less than". But I'm very confused about how to set it up. Would I state Ho:u=47 (null) & H1:u<47 (alt)? And how do I go from there?

If anyone can help (or at least point me in the right direction), I'd appreciate it.

Thanks!
 

Mean Joe

TS Contributor
#2
I know this should be a left-tailed test since it states "less than". But I'm very confused about how to set it up. Would I state Ho:u=47 (null) & H1:u<47 (alt)? And how do I go from there?
Yes, those would be your hypotheses. For hypothesis test and for confidence interval, you need to know sample mean and sample standard deviation (remember to divide by n-1). And then you'll need to calculate standard error of sample mean = sample standard deviation / sqrt(n)

I'm going to use the following abbreviations:
m = sample mean
SEM = standard error of the sample mean

For hypothesis test: do t-test with statistic t = (m - hypothesized mean) / SEM, n-1 df

For confidence interval: m +/- (z-value) * SEM