Step 1: Set up the hypothesis right. The null hypothesis is
easy. It's usually something like
| Our method will make more that 100 widgets per hour | H1: m > 100 |
| This traffic sign will result in less than 4 accidents per month | H1: m < 4 |
| There is a problem if sales fall below $1000 per day | H1: m < 1000 |
| There is a problem if the assembly line has more than 1 defect per hour | H1: m > 1 |
| The bottle volume must be maintained at 250 ml (too much or too little is not good) | H1: m ¹ 250 |
Step 2: Figure out whether to use t or Z. As a general rule of thumb, if the sample size is less than 30 and the problem states that the data is normally distributed, use t with (n-1) degrees of freedom. The exception to the under-30 rule is if the population standard deviation (s) is known and the data is normal. Then you use Z.
Step 3: Find the rejection region. This depends on the direction of the alternative hypothesis.
| > | a in upper tail |
| < | a in lower tail |
| ¹ | Split a between upper/lower tail |
For example, suppose a = 0.05 and we are using Z. Z0.05 = 1.645 and Z0.025 = 1.96.
| > | Reject H0 if Z > 1.645 |
| < | Reject H0 if Z < -1.645 |
| ¹ | Reject H0 if Z > 1.96 or Z < -1.96 |
Step 4: Compute the test statistic and compare it against the critical value. Whether it is Z or t, the statistic is: