Hypothesis Tests for Two Samples

CompetencyFormulate 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 ProfileYou 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 StudiedYour 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.What to SubmitYour research and analysis should be presented on the Word document provided. All calculations should be provided on a separate Excel workbook that should be submitted to your boss as well.
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Deliverable 05 â?? Worksheet
Instructions: The following worksheet describes two examples â?? 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 ð?¥Ì?1 represents the mean blood pressure of the treatment group and ð?¥Ì?2 represents 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
CONTROL GROUP
GROUP
n1
80
n2 70
Ì?
Ì?
ð??ð?
186.7
ð??ð? 201.9
s1
38.5
s2 39.8
1. Write the hypotheses in symbolic form, determine if the test is right-tailed, lefttailed, or two tailed and explain why.
Answer and Explanation
Enter your step-by-step description and explanations here.
2. Calculate the critical value and the test statistic.
Answer and Explanation
Enter your step-by-step description and explanations here.
3. Make a decision about the null hypothesis and explain your reasoning, then make a
conclusion about the claim in nontechnical terms.
Answer and Explanation
Enter your step-by-step description and explanations here.
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
1
2
3
4
5
6
7
8
9
10
11
12
Before
200
174
198
170
179
182
193
209
185
155
169
210
After
191
170
177
167
159
151
176
183
159
145
146
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 hypotheses in symbolic form, determine if the test is right-tailed, left-
tailed, or two tailed and explain why.
Answer and Explanation
Enter your step-by-step description and explanations here.
5. Calculate the test statistic and the P-Value.
Answer and Explanation
Enter your step-by-step description and explanations here.
6. Make a decision about the null hypothesis and explain your reasoning, then make a
conclusion about the claim in nontechnical terms.
Answer and Explanation
Enter your step-by-step description and explanations here.

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