Question: A drug manufacturing company is interested in testing whether their new migraine medicine significantly reduces the length of migraines. Migraines normally last for 35 minutes (with a standard deviation of 10 minutes), and a sample of 49 individuals selected by the company had an average migraine length of 30 minutes. Using an alpha level of 0.05, can the company conclude that those taking the drug have significantly shorter headaches (Conduct a one-tail test)?  Edit

Answer: Null Hypothesis: H0: mu<35 Alternative Hypothesis: mu>=35 Here x bar=30 , n=49 , population sd=10 sample sd=10/sqrt(49)=10/7=1.43 Test statistic,z=(x bar - mu)/sample sd=(30-35)/1.43=-5/1.43=-3.49 at alpha=0.05 , critical z - value for one-tail = +/- 1.65 Since, computed z (-3.49) < critical z(-1.65). So, Null Hypothesis is rejected. Conclusion: Those taking the drug have not significantly shorter headaches.   Edit