# Five Steps of Hypothesis Testing: Statistics

A researcher predicts that listening to music while solving math problems will make a particular brain area more active. To test this, a research participant has her brain scanned while listening to music and solving math problems, and the brain area of interest has a percentage signal change of 58.

From many previous studies with this same math problems procedure (but not listening to music), it is known that the signal change in this brain area is normally distributed with a mean of 35 and a standard deviation of 10.

(a) Using the .01 level, what should the researcher conclude? Solve this problem explicitly using all five steps of hypothesis testing, and illustrate your answer with a sketch showing the comparison distribution, the cutoff (or cutoffs), and the score of the sample on this distribution.

Could you explain your answer to someone who has never had a course in statistics (but who is familiar with mean, standard deviation, and Z scores)?

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Solution

a)

1) Restate the question as a research hypothesis and a null hypothesis about the populations.

There are two populations of interest:

Population 1: People who do math problems while listening to music.

Population 2: People who do math problems in general

The research hypothesis is that the mean signal change in the brain area of Population 1 is greater than that of Population 2.

The null hypothesis is that there is no difference between the two populations.

2) Determine the characteristics of the comparison distribution.

The ...

#### Solution Summary

In this solution we test a hypothesis by applying the five steps of hypothesis testing and thoroughly explain the answer in simple terms.