Medical researchers found that people who take aspirin take on average 8.6 tablets a week. A medical doctor wanted to see if he could reduce the number of aspirin tablets a person consumes if the subjects practiced yoga twice a week. A random sample of 12 people who take aspirin were taught yoga, and after a 12-week period the doctor found that they took an average of 6.8 tablets for one week, with a sample standard deviation 2.37. Test the claim at \(\alpha=0.10\). Assume the variable is normally distributed.

Step 1: 

Write the hypothesis 

\[H_0:\mu=8.6\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; H_1: \mu<8.6 \text{ (claim)}\]

So this is a left-tail test

Step 2:

Since we do not know the population standard deviation we need to look in the t-table for one-tail 0.1 as well we see that our degrees of freedom are: \(df=12-11\) and we get 

Since we are doing a left tail test and our table only gives values for right tail, we need to make our t-value negative:

\[t_{\alpha}=-1.363\]

Step 3:

Calculate the test value

\[\text{Test Value}=\frac{6.8-8.6}{\frac{2.37}{\sqrt{12}}}=-2.63\]

Step 4:

Note

\[-2.63<-1.363\]

So we reject \(H_0\)

Step 5:

Conclusion

There is enough evidence to support the claim.