Probability, Distributions, Hypothesis Testing, and Measures

Probability, Distributions, Hypothesis Testing, and Measures

PART I

Statistical hypothesis testing refers to the statistical methods employed in gaining inference from a set of data. According to Simar and Wilson (2020), the methods are used to develop a suitable conclusion from two sets of contrasting and possibly conflicting hypotheses. The research project is quantitative, and as such, only statistical tests will be conducted to determine the null hypotheses. The research study has formulated two null hypotheses that it intends to test. Both hypotheses pertain to the relationship between the ADA transition plan among public agencies in Florida and post-secondary school transition into employment and marginalized communities and people living with disabilities. The t-test is used to determine the differences between the two means. The test will be appropriate for this study since it is simple and provides an interesting comparison standard. In other words, t-tests are often simple to interpret while the analysis is robust. Besides, the test is also characterized by the ease of collecting data and computation.

Another important test that will be used for the set of null hypotheses is the analysis of variance. The analysis of variance (ANOVA) is one of the most suitable tests to adopt whenever comparing two sets of means (Zhu & Bradic, 2018). Since only one independent variable, the ADA transition plan, will be used in the study, the one-way ANOVA test will be utilized. The Test is suitable as it can control type 1 error and provides the basis for a general comparison of means. The final test used for the questions and null hypothesis testing is Pearson’s t-test. The test is conducted to establish the strength of the relationship between variables. Many researchers consider Pearson’s r test as the best for determining the association between variables. The test also provides information about the magnitude of the relationship. The correlation between the dependent and independent variables will be determined by testing how their means are closely related. For instance, if the mean for ADA transition and the rate of secondary school transition to the job are not closely related, the results from the three tests will show a value of zero. A negative value will mean a weak correlation while a positive value a strong correlation.

PART II

Employed and Unemployed Men and Women age 20 Years and Over in the U.S

Source: U.S Bureau of Labor Statistics.

Contingency Table

Expected Frequencies Table

1.  From the tables, the frequency distribution value is 1. Frequency in statistics refers to the number of times a single value appears in a set of values.

2. The Chi-Square statistic at the significance level of 0.5 equals 5.4035, while the p-value is 0 .020097. Chi-square determines the difference between the observed frequencies and expected frequencies in statistics. The p-value refers to the probability that the observed values could occur randomly.

3. The T-Statistic equals 1.982273. T-Statistic, in simple terms, refers to the differences in the means between two groups in statistics. In this case, the differences in means are taken between the total number of employed and unemployed males and females.

Three main data types are used in statistics, including nominal, ordinal, and continuous data. Nominal data is characterized by variables labeled without any quantitative value or order. On the other hand, Ordinal data have natural ordering with values representing some kind of relative position. The type of data occupies a position between quantitative and qualitative data and cannot be subjected to any form of statistical analysis. Finally, continuous data is often expressed in the form of fractions. The data presented above falls under the category of data referred to as discrete data. Discrete data is separate or distinct and contains values with the whole number such as 80,767, 3,199, 70,857, and 2,637, among others. Since the data is discrete, it cannot be subjected to the three types of tests.

Part III

The two null hypotheses formulated for this research study are as follows:

1. The percentage of local public agencies in Florida with ADA transition plans have no direct impact on post-secondary school transition into employment.
2. The ADA transition plans in Florida have no significant impact on marginalized communities and people living with disabilities.

Since the research study is formulated to be quantitative, the two null hypotheses seem suitable for the study at this point. The reason is that they can easily be tested through the here identified statistical testing methods to provide the required results for analysis. Therefore, the null hypotheses that have been formulated for this quantitative study will not be subjected to any changes.

References

Simar, L., & Wilson, P. W. (2020). Hypothesis testing in nonparametric models of production using multiple sample splits. Journal of Productivity Analysis, 53(3), 287-303.

Zhu, Y., & Bradic, J. (2018). Linear hypothesis testing in dense high-dimensional linear models. Journal of the American Statistical Association, 113(524), 1583-1600.