Gender gap Candidates for political office realize that different levels of supp

Step 1
Hey, since there are multiple subparts posted, we will answer first three subparts. If you want any specific subpart to be answered then please submit that subpart only or specify the subpart in your message.
Given info:
One survey was done on gender gap in voting. It was seen that ${\displaystyle 52\mathrm{\%}}$ of 473 men support him but ${\displaystyle 45\mathrm{\%}}$ of 522 women support him.
Step 2
a) Calculation:
For finding the confidence interval using z-intervals the assumption and conditions should met.
The assumption and conditions for inference:
(i) Randomization condition: Though it is not given that the sample is random but it can be assumed that the poll was random.
(ii) Independent group assumption: The two groups are independent for different gender.
(iii) Success/failure condition: Here for men $npˆ=246\hspace{0.17em}nqˆ=473-246=227$ and for women $npˆ=235\hspace{0.17em}nqˆ=522-235=287$ All are greater than 10.
Hence, all conditions are satisfied for the inference.
Step 3
Confidence interval:
Software procedure:
Step by step procedure to obtain the confidence interval using the MINITAB software:
Choose Stat > Basic Statistics > 1 Proportion.
Choose Summarized data.
In Number of events, enter 246 In Number of trials, enter 473
Click Options. Under Alternative, and choose not equal.
Click OK in each dialog box.
Output using the MINITAB software is given below:
Test and Cl for One Proportion
Method
p: event proportion
Normal approximation method is used for this analysis.
Descriptive Statistics
$\begin{array}{|cccc|}\hline N& \text{Event}& \text{Sample p}& 95\mathrm{\%}\text{CI for p}\\ 473& 246& 0.520085& (0.475,0.565)\\ \hline\end{array}$
Test
Null hypothesis ${\displaystyle H_0:p=0.5}$
Alternative hypothesis ${\displaystyle H_1:p\ne 0.5}$
From the MINITAB output, the ${\displaystyle 95\mathrm{\%}}$ confidence interval is (0.475, 0.565)
Interpretation:
The ${\displaystyle 95\mathrm{\%}}$ confidence interval for the percent of male voters who may vote for this candidate is (0.475, 0.565) means that there is ${\displaystyle 95\mathrm{\%}}$ confident that the percentage of men who will vote him lies between ${\displaystyle 47.5\mathrm{\%}}$ and ${\displaystyle 45.5\mathrm{\%}}$.
Step 4
(b) Confidence interval:
Software procedure:
Step by step procedure to obtain the confidence interval using the MINITAB software:
Choose Stat > Basic Statistics > 1 Proportion.
Choose Summarized data.
In Number of events, enter 235 In Number of trials, enter 522
Click Options. Under Alternative, and choose not equal.
Click OK in each dialog box.
Output using the MINITAB software is given below:
Test and CI for One Proportion
Method
p: event proportion
Normal approximation method is used for this analysis.
Descriptive Statistics
$\begin{array}{|cccc|}\hline N& \text{Event}& \text{Sample p}& 95\mathrm{\%}\text{CI for p}\\ 522& 235& 0.450192& (0.4075,0.4929)\\ \hline\end{array}$
From the MINITAB output, the ${\displaystyle 95\mathrm{\%}}$ confidence interval is (0.4075, 0.4929)
Interpretation:
The ${\displaystyle 95\mathrm{\%}}$ confidence interval for the percent of female voters who may vote for this candidate is (0.4070, 0.4929) means that there is ${\displaystyle 95\mathrm{\%}}$ confident that the percentage of men who will vote him lies between ${\displaystyle 40.75\mathrm{\%}}$ and ${\displaystyle 49.29\mathrm{\%}}$.
Step 5
(c) From part a, the ${\displaystyle 95\mathrm{\%}}$ confidence interval for the percent of male voters who may vote for this candidate is (0.475, 0.565)
From part a, the ${\displaystyle 95\mathrm{\%}}$ confidence interval for the percent of female voters who may vote for this candidate is (0.4070, 0.4929)
From the two outputs, it can be said that the confidence intervals overlap.
Hence, there is no evidence to support that the proportion of male and female will differ for voting him.