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## Choosing a Statistical Test

You will complete the “Choosing a Statistical Test assignment #1” as a summative activity. Read the entire assignment prior to starting to work.Open the data set on “Percent of Adults with College Degree or Higher by County in Alabama”. You will then choose and conduct the appropriate statistical analyses to best answer the questions based on the scenario provided. Each question is worth 5 points; however, partial credit may be awarded if answers are not complete.
1. Round statistics to two decimal places.
2. Use correct abbreviations and reporting format for the statistic followed by the answer.
Example: SD = 1.23

## Computing Central Tendency

A community leader in a small rural county in Alabama read an article “67 Alabama Counties, Ranked from Most to Least-educated” published by AL.Com (2017). After reading this article, he became interested in determining two things: 1) an overview of education in the Alabama counties and 2) how well Alabama counties compared to the national average of college level educated adults. National average = 33%.
1. What is the mean percent of adults with a college degree or higher in Alabama?
2. What is the median percent of adults with a college degree or higher in Alabama?
3. What is the lowest percent of adults with a college degree or higher in Alabama? Which county had the lowest percent?
4. What is the highest percent of adults with a college degree or higher in Alabama? Which county had the highest percent?
5. What is the value of the range?
6. What is the value of the standard deviation?
7. What is the value of the skewness statistic? Is this value computed by SPSS supported by a comparison of the mean and median? Explain.
8. What are the values of the 30th, 60th, and 90thpercentiles? Write a statement illustrating your interpretation of the 30th percentile.
9. What is the appropriate statistical test to how well Alabama counties compared to the national average of college level educated adults?

## Hypothesis Testing

10. a. Write an acceptable null hypothesis using written statement form for this statistical test.
b. Write an acceptable research or alternative non-directional hypothesis.
c. Write an acceptable research or alternative directional hypothesis.
11. What is the computed value of the test statistic? (do not round)
12. What is the value of the degrees of freedom that are reported in the output)?
13. What is the reported level of significance? (do not round)
14. Based on the reported level of significance, would you reject the null hypothesis? What would be the appropriate conclusion?
15. What is the reported confidence interval? Interpret this.

Solution to Assignment Scenario: A community leader in a small rural county in Alabama read an article “67 Alabama Counties, Ranked from Most to Least-educated” published by AL.Com (2017). After reading this article, he became interested in determining two things: 1) an overview of education in the Alabama counties and 2) how well Alabama counties compared to the national average of college level educated adults. National average = 33%.  The mean percent of adults with a college degree or higher in Alabama is 16.65%  The median percent of adults with a college degree or higher in Alabama 14.10%  The lowest percent of adults with a college degree or higher in Alabama is 8.20% while the country with the lowest percent is Conecub  The highest percent of adults with a college degree or higher in Alabama is 40.80% while the country with the lowest percent is Shelby  The range value is 32.60  The standard deviation is 7.04  The skewness statistic is 1.68. If the skewness is less than -1 or greater than 1, the data are highly skewed. Therefore, since the skewness statistic is greater than 1, we say that the data is highly skewed.  The values of the 30th, 60th, and 90th percentiles are 12.44, 15.54, and 28.60 respectively. Percentiles tell you how a value compares to other values. The 30th percentile means 12.44% in adults with a college degree or higher in Alabama contribute about 30% of the education percentage.  The appropriate statistical test to show how well Alabama counties compared to the national average of college level educated adults is the One-sample t-test  Null Hypothesis (H0): there is no statistical difference in the sample mean and the hypothesized mean (33.00) i.e. H_0: μ≠μ_0 Alternative Hypothesis (H0): there is statistical difference in the sample mean and the hypothesized mean (33.00) i.e. H_0: μ=μ_0 Alternative Hypothesis (H0): there is statistical difference in the sample mean and the hypothesized mean (33.00) i.e. H_0: μ>μ_0  The computed value of the test statistics is -18.996  The value of the degrees of freedom reported in the output is 66  The reported level of significance is 0.000  Based on the output, the null hypothesis will be rejected as the test is statistically significant because the level of significance is less than 0.05. Therefore, we conclude that there is statistical difference between the sample mean and the hypothesized mean (33.00). The reported confidence interval is (-18.06, -14.63). This shows that the researcher is 95% confident that the population parameter is between -18.06 and -14.63.