Testing Hypothesis for Means

The scenario focuses on assessing whether a series of reforms have increased African’s democracy views. In other words, it is assessing the effectiveness of the reforms in influencing the democracy views of the Africans. The null hypothesis is that the mean perceptions (views) are not different from 6 while the alternative hypothesis is that the mean perceptions was different from 6, based on a 1-10 scale. A one-sample t-test analysis was suitable in this case.

Table 1

T-test for a single mean 

The series of reforms had a significant effect on the democracy perceptions of Africans. The mean perceptions score was statistically different from 6, t 46,939 = -35.924, p < 0.05. In this case, the observed p-value was less than 0.05 indicating that the null hypothesis was rejected (Wilcox, 2017). Such an aspect indicates that, the African’s perceptions on democracy can be effectively manipulated through the reforms.

Scenario 2 

Based on the above findings, the study also focused to assess if the mean perception scores in democracy today varied between the South African and North American regions. The null hypothesis supposes that the mean democracy perception scores are equal between the two regions while the alternative hypothesis supposes that the two regions have different mean scores.

Table 2

T-test on two independent means 

The mean democracy perception scores between Northern and Southern African regions were statistically different from each other, F 21,395 = 130.649, p < 0.05. The Southern Africa had a higher democracy perception mean score than the Northern Africa and this implies that, the recent social change movements in North Africa have been effective in influencing the people on democracy.

Scenario 3 

The study focuses to assess if the perceptions of students regarding mathematical utility have changed between their freshman and senior years. The paired-sample t-test is appropriate for this study because scores are matched for the same respondents (Wagner, 2016).

Table 3

Paired t-test analysis 

Based on the analysis, the mean scores on the mathematical utility in freshman and senior years were not statistically different from each other, t 16,020 = -1.649, p > 0.05. The p-value is greater the alpha and the null hypothesis was not rejected (Frankfort-Nachmias & Leon-Guerrero, 2018). High school perceptions on mathematical utility was not influenced by the year of study in the college.

References 

Frankfort-Nachmias, C., & Leon-Guerrero, A. (2018). Social statistics for a diverse society (8th ed.). Thousand Oaks, CA: Sage Publications.

Wagner, W. E. (2016). Using IBM® SPSS® statistics for research methods and social science statistics (6th ed.). Thousand Oaks, CA: Sage Publications.

Wilcox, R. R. (2017). Introduction to robust estimation and hypothesis testing . Amsterdam; Heidelberg: Elsevier, Academic Press.