Using Elementary Statistics to Predict Presidential Outcome

Elementary Statistics is a discipline of mathematics concerned with the collection, organization, analysis, presentation, and interpretation of quantitative data to aid with drawing useful insights and with the making of informed decisions. In an elementary statistics class, students study data and graphs, prepare and analyze experiments, and decide whether the results obtained from various studies are valid or not.

Measures of central tendency

Mean for the year that people think that the first female president will be elected, for all DEMOCRATS =2020.73
Standard deviation for the year that people think that the first female president will be elected, for all DEMOCRATS =9.224
N=109
Confidence interval=(mean-std*t/sqrt(n),mean+std*t/sqrt(n))
95%CI=( 2020.73- 9.224*1.96/sqrt(109), 2020.73 + 9.224*1.96/sqrt(109))
95%CI=(2018.98,2022.46)
Correlation=-0.0596
t-statistics=-0.964
p-value=0.3359(>0.05) therefore we can conclude that there is no association between the age of an individual and the year he/she think when there will be the first woman president.

Regression analysis

For the equation of the regression
Coefficients:
(Intercept) Age
 2022.92 -0.04676
Interpretation-Coefficient of age is -0.04676 which means that for a unit increase in age the expected year when there will be the first woman president decreases by 0.04676 units. Since age can never be 0 so intercept is non-interpretable.
Year=2022.92-0.04676 * Age
On substituting Age=52.
Year=2022.92-0.04676 *52=2020.488
We can use one way ANOVA to test if the predicted year that the first female president will be elected is associated with the respondent’s political party affiliation. If you would like our experts to assist you with this topic, take our regression analysis assignment help.

Hypothesis Testing

Null Hypothesis: Mean predicted year that the first female president will be elected is the same for the respondent of all the parties.
Alternate Hypothesis: Mean predicted the year that the first female president will be elected is different for the at-least respondent of one party from others.
 
ANOVA Table
Df Sum Sq Mean Sq F P-value
Your.Party 4 1350 337.4 2.991 0.0194
Residuals 259 29219 112.8
Since, p-value=0.0194(<0.05). we can reject the Null hypothesis and conclude that the predicted year that the first female president will be elected is associated with the respondent’s political party affiliation.
Your.Party Mean_Year
Independent 2018.642
Democrat 2020.734
Republican 2022.717
Other 2025.217
Therefore, we can see that the Other has the latest predicted year and Independent have the earliest predicted year.

Null Hypothesis: Males and females have the same predicted year that the first female would be elected president

Alternative Hypothesis: Males and females have a significantly different predicted year that the first female would be elected president.

The variable of interest will be the mean predicted year for males and females.

mean in group Female mean in group Male

            2020.348 2022.624

t = -1.6822, p-value = 0.09398

since p-value=0.09398(>0.05) we fail to reject the null hypothesis and conclude that males and females do not have a significantly different predicted year that the first female would be elected president.


Year for Female Year for Male
Min. 2012 2012
1st Qu 2016 2016
Median 2020 2020
Mean 2020 2023
3rd Qu 2020 2024
Max. 2072 2072
For females distribution of the year when the first female president will be elected is negatively skewed. For males distribution of the year when the first female president will be elected is symmetric. Null Hypothesis: The proportions of the different political parties are all equal Alternative Hypothesis:The proportions of the different political parties are not all equal. We can conduct a chi-square test to check this claim.

Descriptives:             observed freq. expected freq. specified prob.

Democrat               178          71.25            0.25

Independent             27          71.25            0.25

Other                   12          71.25            0.25

Republican              68          71.25            0.25

Since out of 287 entries 6 are null

Test results:    

X-squared statistic:  236.839    

degrees of freedom:  3    

p-value:  <.001

since the p-value is less than 0.05 we can reject the null hypothesis and can conclude that the proportions of the different political parties are not all equal.

Null Hypothesis:the proportion of people feeling that the first female president will be a democrat (labeled “Candidate Party”) is the same for males and females.i.e p=0.5

Alternative Hypothesis:the proportion of people feeling that the first female president will be a democrat (labeled “Candidate Party”) is lower for males than females.i.e, p>0.5

Variable of interest::the proportion of Females feeling that the first female president will be a democrat (labeled “Candidate Party”)

Descriptives:        observed freq. expected freq. specified prob.

Female             91           88.5             0.5

Male               86           88.5             0.5 p=0.5141 z=0.376

p-value=0.3535(>0.05). Therefore we fail to reject the Null Hypothesis and conclude that proportion of people feeling that the first female president will be a democrat (labeled “Candidate Party”) is not lower for males than females. Null Hypothesis: political party of the respondent (labeled “Your Party”) is not associated with the political party of the first female president (labeled “Candidate Party”) Alternative Hypothesis: political party of the respondent (labeled “Your Party”) is associated with the political party of the first female president (labeled “Candidate Party”)

Candidate Part
YourParty Democrat Independent Other Republican
Democrat 92 6 1 14
Independent 29 9 1 14
Other 25 7 7 13
Republican 29 4 3 27
Pearson's Chi-squared test

X-squared = 54.045, df = 16, p-value = 5.098e-06

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