Writing conclusions

For problems involving comparison of two parameters (two means or two proportions)

Example: Scrapie is a "wasting disease" which affects sheep and goats. Studies of scrapie are sometimes conducted on mice or hamsters. A certain drug has been proposed as a treatment for this disease, which is expected to prolong the life of treated mice. A study is done in which 30 infected mice are randomly assigned to a treatment and a control group, and their remaining lifetime (in days) is recorded. (The subjects have been infected for a month at the time the experiment begins.)

For the following data, first do a hypothesis test to determine whether the drug increased the mean lifetime and then set up and interpret a confidence interval to estimate the size of the treatment effect on the average remaining lifetimes.

Group	sample mean	sample st dev	sample size
Drug (Treatment)	111.7	16.3	15
No Drug (Control)	89.9	6.9	15

For either a hypothesis test or confidence interval, we must define the parameters.

= mean remaining lifetime of all infected mice if they had no treatment.

= mean remaining lifetime of all infected mice if they had treatment with this drug.

Either of the two solutions below (left and right) is correct. Both are provided to illustrate that there are different correct ways to write these and so that you can see the similarities and differences between those correct ways.

Using the conservative df = 14, the P-value is 0.000149. These data provide significant evidence, at the 5% level, that .	Using the conservative df = 14, the P-value is 0.000149. These data provide significant evidence, at the 5% level, that .
I have 95% confidence that is between and days.	I have 95% confidence that is between 12.2 and 31.4 days.

All of these are correct interpretations of the hypothesis test or confidence interval and students should be able to write any of these, and to recognize any of these as correct.

The data provide significant evidence, at the 5% level, that the average lifetime of the population of infected mice without treatment is shorter than the average lifetime of the population of infected mice with treatment.

The data provide significant evidence, at the 5% level, that the average lifetime of the population of infected mice with treatment is longer than the average lifetime of the population of infected mice without treatment.

 I have 95% confidence that is less than by between 12.2 and 31.4 days.

I have 95% confidence that is greater than by between 12.2 and 31.4 days.

I have 95% confidence that the mean remaining lifetime of the population of infected mice with treatment is between 12.2 and 31.4 days longer than the mean remaining lifetime of the population of infected mice without treatment.

I have 95% confidence that the mean remaining lifetime of the population of infected mice without treatment is shorter by between 12.2 and 31.4 days than the mean remaining lifetime of the population of infected mice with treatment.

I have 95% confidence that, on the average, infected mice with treatment live longer by 12.2 to 31.4 days than infected mice without treatment.

Footnote:

The following interpretation is mathematically correct, but a person who writes this looks as if he doesn’t really understand the situation.

 I have 95% confidence that is greater than by between and days.