# Inferential Statistics to Analyze Data

In Assessment 1, you documented typical responses to your survey, along with your question formulations. You did not know it at the time, but you were hypothesizing about the future survey results. Now that you have survey data, you can go back and apply the tools of inferential statistics to test your hypotheses.

For this assessment, analyze data using inferential statistics for your previously defined survey questions. Before you begin your analysis, note the following:

Use the population proportions for questions 14 and the population means for questions 56. The sample statistics were calculated for each survey question in Assessment 2. Use this prior work to help complete this assessment. Keep in mind that you have already calculated the sample proportions for questions 14 as well as the sample means and standard deviations for questions 56.
Use the Inferential Statistics to Analyze Data Template located in the Resources under the Required Resources heading. The template has two pages. Be sure to review each one carefully. The first page is the blank template that you will complete, and the second page is a completed example. Almost every type of situation is shown, so try to model your results after the ones shown.
Directions
Calculate a 95% confidence interval for each of your survey questions (16). Your final product should have six confidence intervals.
Perform a hypothesis test for each survey question (16). Your final product should have six hypothesis tests.
When determining the two hypotheses for each question, how do you know what to compare the population parameter to? Honestly, we do not know, but we can make an educated guess. First, since we have sample proportions and means to consider, remember that the sample statistics always support the alternative hypothesis. Why? Hypothesis testing always tries to reject the null hypothesis; thus, we must have some evidence (the sample statistics) that the alternative is correct. Outside of this requirement, feel free to use any logical value in your hypothesis test.

A few notes, however:

We always think the alternative hypothesis is correct! This means the sample statistics (the sample proportion or mean) support the alternative hypothesis.
You probably want to write the alternative hypothesis first. Then, the null hypothesis is just the opposite of the alternative.
The two hypotheses must be the exact opposites of each other. We cannot put one value for the null and another for the alternative; that simply is not logical.
For questions 14, we are using the sample proportion to estimate the population proportion. For questions 56, we are using the sample mean to estimate the population mean. Thus, we use different formulas for their confidence intervals and for their test statistics in the hypothesis tests.

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