Competency Assignment
Formulate and evaluate hypothesis tests for population parameters based on sample statistics using both Critical Regions and P-Values, and be able to state results in a non-technical way that can be understood by consumers of the data instead of statisticians.
Student Profile
You are a statistician working for a drug company. A few new scientists have been hired by your company. They are experts in pharmacology, but are not experts in doing statistical studies, so you will explain to them how statistical studies are done when testing two samples for the effectiveness of a new drug. The two samples can be dependent or independent, and you will explain the difference.
Concept being Studied
Your focus is on hypothesis tests and confidence intervals for two populations using two samples, some of which are independent and some of which are dependent. These concepts are an extension of hypothesis testing and confidence intervals which use statistics from one sample to make conclusions about population parameters.
Worksheet
Instructions: The following worksheet describes two examples - one is an example for independent samples and the other one for dependent samples. Your job is to demonstrate the solution to each scenario by showing how to work through each example in detail. You are expected to explain all of the steps in your own words.
Independent samples:
One of our researchers wishes to determine whether people with high blood pressure can reduce their systolic blood pressure by taking a new drug we have developed. The sample data is shown below, where x ¯_1represents the mean blood pressure of the treatment group and x ¯_2represents the mean for the control group. Use a significance level of 0.01 and the critical value method to test the claim that the drug reduces the blood pressure. We do not know the values of the population standard deviations.
|
Treatment Group
|
Control Group
|
|
n1
|
80
|
n2
|
70
|
| x ¯_1 |
186.7
|
x ¯_2 |
201.9
|
|
s1
|
38.5
|
s2
|
39.8
|
1. Write the hypotheses in symbolic form, determine if the test is right-tailed, left-tailed, or two tailed and explain why.
2. Calculate the critical value and the test statistic.
3. Make a decision about the null hypothesis and explain your reasoning, then make a conclusion about the claim in nontechnical terms.
Dependent samples
This same new drug was tested on another group, but this time the test was done before the drug was administered, and then tested after the drug was given to the same group.The results are shown in the table below:
|
Subject
|
Before
|
After
|
|
1
|
200
|
191
|
|
2
|
174
|
170
|
|
3
|
198
|
177
|
|
4
|
170
|
167
|
|
5
|
179
|
159
|
|
6
|
182
|
151
|
|
7
|
193
|
176
|
|
8
|
209
|
183
|
|
9
|
185
|
159
|
|
10
|
155
|
145
|
|
11
|
169
|
146
|
|
12
|
210
|
177
|
Use the data above with a significance level of 0.05 to test the claim that for the populations of blood pressures before and after the drug, the differences have a mean greater than 0 mm Hg (so the claim is that the drug helps lower the blood pressure). Use the P-Value method to determine whether or not to reject the null hypothesis and state your conclusion.
4. Write the hypothesesin symbolic form, determine if the test is right-tailed, left-tailed, or two tailed and explain why.
5. Calculate the test statistic and the P-Value.
6. Make a decision about the null hypothesis and explain your reasoning, then make a conclusion about the claim in nontechnical terms.