Given a data set that can be graphed as a standard normal curve, respond to the prompts below.

1. What defines the graph? I.e., what determines the shape of the graph and what is the relationship between these defining characteristics?
2. What must be done in order to transform a normal distribution of data into a standard normal distribution based on the same data?
3. What is the advantage of having transformed data so that it can be represented by a standard normal distribution?
4. We often see data points represented by either x or z. What is the relationship between them?
5. Why is the area under the standard normal curve above the mean always the same value?

A social worker notes that in a population of psychiatric inpatients the ethnic mix seems out of balance with what she has understood to be the ratios in the general population. Respond to the prompts below to show how she might determine whether the inpatient ethnic mix varies from the mix in the general population.

1. What statistical test would be appropriate to use here? Explain the rationale for your answer.
2. What assumptions would need to be met in order to use the test?
3. Describe the data that the test would be based on as either quantitative or qualitative. Explain the rationale for your answer.
4. Give an example of how the null and alternative hypotheses for this test could be stated.
5. What would the researcher need to know in order to calculate the appropriate test statistic? I.e., what values need to be known or calculated in order to complete the calculation of the test statistic?