A clinical investigator has developed two new treatments (treatment A and B) for

Question

A clinical investigator has developed two new treatments (treatment A and B) for high cholesterol. The investigator is not sure which treatment will significantly reduce the average cholesterol level. There were a total of 140 people randomized into the two treatments but some of the participants dropped from treatment B. The investigator wants the level of significance to be fairly stringent at 5%.

1. State the hypothesis the investigator wants to tests. Use mathematics notation (i.e. H0 and HA)

2. What is the additional condition required to use the pooled t-test? Are these met? If not, which test should you use?

Explanation / Answer

State the Hypotheses

Every hypothesis test requires the analyst to state a null hypothesis and an alternative hypothesis. The hypotheses are stated in such a way that they are mutually exclusive. That is, if one is true, the other must be false; and vice versa.

The table below shows three sets of null and alternative hypotheses. Each makes a statement about the difference d between the mean of one population 1 and the mean of another population 2. (In the table, the symbol means " not equal to ".)

The first set of hypotheses (Set 1) is an example of a two-tailed test, since an extreme value on either side of the sampling distribution would cause a researcher to reject the null hypothesis. The other two sets of hypotheses (Sets 2 and 3) are one-tailed tests, since an extreme value on only one side of the sampling distribution would cause a researcher to reject the null hypothesis.

When the null hypothesis states that there is no difference between the two population means (i.e., d = 0), the null and alternative hypothesis are often stated in the following form.

H0: 1 = 2
Ha: 1 2

Set Null hypothesis Alternative hypothesis Number of tails 1 1 - 2 = d 1 - 2 d 2 2 1 - 2> d 1 - 2 < d 1 3 1 - 2< d 1 - 2 > d 1

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