# Inferential Statistics To Analyze Data

Analyze data using inferential statistics for your previously defined survey questions.

##### Required Resources

The following resources are required to complete the assessment.

###### Capella Resources

Click the links provided to view the following resources:

##### Suggested Resources

The following optional resources are provided to support you in completing the assessment or to provide a helpful context. For additional resources, refer to the Research Resources and Supplemental Resources in the left navigation menu of your courseroom.

###### Capella Resources

Click the links provided to view the following resources:

- Statistics Terminology.
- This site from Capella iGuide includes sections on null hypothesis, alternative hypothesis, and one-tailed hypothesis.

- Computations.
- This site from Capella iGuide includes a section on
*t*tests.

- This site from Capella iGuide includes a section on
- Interpreting Statistical Data.
- This site from Capella iGuide includes sections on hypotheses, alpha, and
*p*value.

- This site from Capella iGuide includes sections on hypotheses, alpha, and

###### Library Resources

The following e-books from the Capella University Library are linked directly in this course:

- Naghshpour, S. (2012).
*Statistics for economics*. New York, NY: Business Expert Press.- Chapter 6, “Point and Interval Estimation,” pages 119–140. This chapter is about confidence intervals.
- Chapter 7, “Statistical Inference With Test of Hypothesis,” pages 141–161.

- Scott, I., & Mazhindu, D. (Eds.). (2005).
*Statistics for health care professionals*. Thousand Oaks, CA: Sage Publications.- “Displaying Data,” pages 60–72.

- Spiegel, M. R., & Stephens, L. J. (1999).
*Schaum’s outline of theory and problems of statistics*. New York, NY: McGraw-Hill.- Chapter 10, “Statistical Decision Theory,” pages 216–241. This chapter is about hypothesis testing.

- Urdan, T. C. (2005).
*Statistics in plain English*(2nd ed.). Mahwah, NJ: Lawrence Erlbaum.- Chapter 9, “
*t*Tests,” pages 89–100.

- Chapter 9, “
- Weinberg, G. H. (2012).
*Statistics: An intuitive approach*. Belmont, CA: Wadsworth Publishing.- Chapter 12, “The Hypothesis-Testing Procedure,” pages 154–172.

###### Course Library Guide

A Capella University library guide has been created specifically for your use in this course. You are encouraged to refer to the resources in the MAT-FP2001 – Statistical Reasoning Library Guide to help direct your research.

###### Internet Resources

Access the following resources by clicking the links provided. Please note that URLs change frequently. Permissions for the following links have been either granted or deemed appropriate for educational use at the time of course publication.

- Brown, A. (2013). Unit9 a2CL [Video] | Transcript. Retrieved from http://www.youtube.com/watch?v=XNUo06ud6-A&feature=youtu.be
- This 8-minute video provides a helpful overview of an assessment from another course very similar to what you will be completing in this assessment. This video focuses on confidence intervals.

- Brown, A. (2013). Unit9 a2HT [Video] | Transcript. Retrieved from http://www.youtube.com/watch?v=lXD9v2wsaG8&feature=youtu.be
- This 20-minute video provides a helpful overview of an assessment from another course very similar to what you will be completing in this assessment. This video focuses on hypothesis testing.

- Easton, V. J., & McColl, J. H. (n.d.). Statistics glossary. Retrieved from http://www.stats.gla.ac.uk/steps/glossary/index.html
- Khan Academy. (2014). Retrieved from https://www.khanacademy.org
- This Web site offers resources on a range of subjects, including probability and statistics. Search for “descriptive statistics” to find related resources.

- Lane, D. M. (n.d.). Online statistics education: A multimedia course of study. Retrieved from http://onlinestatbook.com/2/index.html
- StatSoft, Inc. (2013). Electronic statistics textbook. Tulsa, OK: Author. Retrieved from http://www.statsoft.com/Textbook
- StatTrek.com. (2014). Statistics tutorial. Retrieved from http://stattrek.com/tutorials/statistics-tutorial.aspx

###### Bookstore Resources

The resource listed below is relevant to the topics and assessments in this course and is not required. Unless noted otherwise, this resource is available for purchase from the Capella University Bookstore. When searching the bookstore, be sure to look for the Course ID with the specific *–FP* (FlexPath) course designation.

- Bennett, J. O., Briggs, W. L., & Triola, M. F. (2014).
*Statistical reasoning for everyday life*(4th ed.). Boston, MA: Pearson.

#### Assessment Instructions

*Note*: Be sure to complete Assessment 3 before completing this assessment.

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 1–4 and the population means for questions 5–6. 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 1–4 as well as the sample means and standard deviations for questions 5–6.
- 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 (1–6). Your final product should have six confidence intervals.
- Perform a hypothesis test for each survey question (1–6). 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 1–4, we are using the sample proportion to estimate the population proportion. For questions 5–6, 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.

## Inferential Statistics to Analyze Data Scoring Guide

ACTIVITY |
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Compute 95% confidence intervals correctly for multiple variables in a study. |

Derive appropriate conclusions based upon calculated confidence intervals for a study. |

Choose appropriate hypothesis tests based upon the context of the questions asked. |

Specify correct null and alternative hypotheses. |

Calculate hypothesis tests correctly for multiple questions in a study. |

Derive appropriate conclusions regarding hypotheses according to the results of hypothesis tests. |