Chapters 9 and 10 in the textbook describe the different criteria for a one-samp
ID: 3053378 • Letter: C
Question
Chapters 9 and 10 in the textbook describe the different criteria for a one-sample hypothesis test and a two-sample hypothesis test.
"In hypothesis testing, you reject the null hypothesis when the sample evidence suggests that it is far more likely that the alternative hypothesis is true. However, failure to reject the null hypothesis is not proof that it is true. You can never prove that the null hypothesis is correct because the decision is based only on the sample information, not on the entire population. Therefore, if you fail to reject the null hypothesis, you can only conclude that there is insufficient evidence to warrant its rejection (p. 286)."
Give an example of a scenario that would warrant either a one-sample or a two-sample test. This can be a hypothetical example.
Please state H0 and H1 and explain why your hypothetical example qualifies as either a one- or two-sample test. (Please recognize that one- and two-sample tests are not the same as one- or two-tail tests.) Also, clearly state the reason(s) this hypothesis test would be conducted.
Explanation / Answer
One Sample Test
You use a 1-sample t-test to assess the difference between a sample mean and the value of the null hypothesis.
Example: A random sample of heterosexual married couples is chosen. Each spouse of each pair takes a survey on marital happiness. The intent is to compare husbands' and wives' scores.
The two-sample t-test would compare the average of the husband's scores with the average of the wives' scores. However, the samples of husbands and wives are not independent -- whatever factors influence a particular husband's score may influence his wife's score, and vice versa. Thus the independence assumption between groups for a two-sample t-test is violated.
In this example, we can instead consider the individual differences in scores for each couple: (husband's score) - (wife's score). If the questions of interest can be expressed in terms of these differences, then we can consider using the one-sample t-test
Two sample test
A paired t-test takes paired observations (like before and after), subtracts one from the other, and conducts a 1-sample t-test on the differences. Typically, a paired t-test determines whether the paired differences are significantly different from zero.
Example: A test is given to each subject before and after a certain treatment. (For example, a blood test before and after receiving a medical treatment; or a subject matter test before and after a lesson on that subject)
The solution is analyze the difference in scores.