Hypothesis Testing Lab

OBJECTIVES: This lab is designed to show you how to generate and interpret hypothesis tests, by analyzing four scenarios. In each of the examples, you will be testing the population mean when the population variance is known.

DIRECTIONS: Follow the instructions below, answering all questions.

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First, please describe the basic purpose of hypothesis testing here:

In general, what is the null hypothesis, and how does a significance test relate to the null hypothesis?

Similarly, what is the purpose of the alternative hypothesis?

What are the three options for an alternative hypothesis?

Discuss what is meant by a P-value, and in particular, how it relates to the null hypothesis.

What is meant by the term “statistically significant”? What is a significance level?

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Now, practice interpreting the Results of a hypothesis test.

A hypothesis is put forward that children who take vitamin C are less likely to become ill during flu season than those who do not. A hypothesis test is conducted where a sample group of children is given vitamin C for three months while another group is not. As it turns out, the alternative hypothesis is confirmed. What does this mean?

Most redheads, a hypothesis suggests, are insecure about their hair color. A hypothesis test is conducted wherein redheads are given polygraph testing to determine how they feel about their hair color. In the end, the alternative hypothesis is rejected when the data shows that most redheads are comfortable with their hair color. What does this mean?

One scientist makes an alternative hypothesis that, contrary to popular belief, young boys are not necessarily prone to more behavioral problems than young girls. Testing confirms the alternative hypothesis – that young boys and young girls are of similar temperament. What does this mean?

Hypothesis testing of the null hypothesis that being out in the cold weather can cause a person to get sick suggests that, in opposition to the old wives’ tale, an individual will not necessarily become ill by staying outside in the cold. What does this mean?

Bonus!

Explain the difference between Type I and Type II errors, and how they relate to the significance level of a study.