9.1 Quick revision
Some of the summary information regarding the number of decayed, missing and filled teeth (DMFT) is shown below. The researchers wanted to compare the mean DMFT for coeliacs and non-coeliacs.
| Sample size | Mean | Standard deviation | Standard error | |
|---|---|---|---|---|
| Coeliac (C) | 23 | 8.39 | 4.4 | 0.92 |
| Non-coeliac (NC) | 23 | 8.17 | 4.1 | 0.86 |
| Difference | 0.22 | 1.3 |
An exact \(95\)% CI is given as for the difference is \(-2.32\) to \(2.76\).
- Using the \(68\)--\(95\)--\(99.7\) rule gives a slightly different CI. Why?
- True or false: The difference is computed as the number of DMFT for coeliacs minus non-coeliacs.
- True or false: One of the values for the CI is a negative value, which must be an error, since a negative number of DMFT is impossible.
- We are \(95\)% confident that the difference between the population means is:
- True or false: The null hypothesis is \(H_0\): \(\mu_{C} - \mu_{NC} = 0\).
- True or false: The alternative hypothesis is \(H_0\): \(\mu_{C} - \mu_{NC} > 0\).
- True or false: Since the two sample means are different, we reject the null hypothesis.
- Suppose the difference between the means was computed as \(\mu_C - \mu_{NC}\). What does this measure?
- Both samples sizes are less than \(25\). What does this mean for the statistical validity of the CI?