The researchers examined the mean age of the patients who were depressed and those who were not. Write an appropriate null and alternative hypothesis. What would be a good statistical test for this analysis and why? The corresponding p value is 0.25? What do you conclude?

Answer:

The null hypothesis would be :

The mean age of patients who are depressed is same as the mean age of the patients who are not depressed

i.e. 

The alternative hypothesis would be

The The mean age of patients who are depressed is different from the mean age of the patients who are not depressed.

i.e. 

A good statistical test for this analysis would be:

T test for two independent samples.

Since the population standard deviation is unknown and for a large enough sample the assumption of normality shall hold, this is a good test for the required analysis.

The corresponding p value is 0.25. We would conclude that since p-value > level of significance(all the common level of significance - 1%,5%,10%), therefore we would not reject the null hypothesis and conclude that there is no significant difference between the mean age of people who are depressed and mean age of people who are not. In other words, we would accept the null hypothesis.