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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.

What to Submit

To complete this assignment, you must first download the worksheet and then complete it.

You will also develop a PowerPoint presentation for the newly hired scientists on these topics, and you have been asked to provide two real-life examples that you will describe step-by-step. Your boss has asked you to include the following slides:

Slide 1: Title slide

Slide 2: Describes the two differences between independent and dependent samples

Slide 3: Provides an example of independent samples when testing a new drug

Slide 4: Shows how to set up a hypothesis test for two independent proportions: One to test whether they are equal and another one to test whether one proportion is larger than the other

Slide 5: Shows the formula for the test statistic for two independent proportions and lists what each variable in the formula represents

Slide 6: Shows the formula for the margin of error (E) when doing a confidence interval on two proportions and explains what each variable stands for

Slide 7: Other than proportions, describes what other types of hypothesis tests can be done for two independent samples

Slide 8: Provides an example of dependent samples (also known as matched pairs) when testing a new drug. The two samples should be a before and after test with the same group

Slide 9: Shows the t formula for the test statistic for matched pairs and explains what each variable represents

Slide 10: Show what a confidence interval for matched pairs would look like using only variables. Also, include the formula for the Margin of Error and state what each variable represents

To show the formulas above, you may need to use the following variables which you can copy from here:

x̅, p̂, q̂, p̅, q̅, d̅, ∑, μ, σ, σ2, α

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