When Amazon workers were negotiating for a Union, a reporter wondered if at least half of Americans support them forming a union.

a) What should be the null and alternative hypotheses to test the reporters claim?

b) Describe type I and type II errors in the context of the problem.

c) A union official decides they will conduct a simulation based on a small sample size.

Below are the simulation results based on many, many simulated samples.

If at least 15 people in the simulated sample of 20 people support them forming a union, they will reject the null hypothesis.

Using the simulation results provided, estimate the probability of committing a type I error. Using the values in the table, explain how you determined the probability.

Suppose the true proportion of those in the population that support Amazon workers forming a union is 80%. Use the simulation results provided to estimate the probability of committing a type II error. Using the values in the table, explain how you determined the probability.

Please teach me using R

\begin{tabular}{|c|c|c|c|} \hline & \multicolumn{3}{|c|}{ Proportion of simulated samples } \\ \hline Number of people in favor of union & p=0.5 & p=0.65 & p=0.8 \\ \hline 0 & 0 & 0 & 0 \\ \hline 1 & 0 & 0 & 0 \\ \hline 2 & 0.0003 & 0 & 0 \\ \hline 3 & 0.0013 & 0.0001 & 0 \\ \hline 4 & 0.0044 & 0 & 0 \\ \hline 5 & 0.0161 & 0 & 0 \\ \hline 6 & 0.0373 & 0.0018 & 0 \\ \hline 7 & 0.0721 & 0.005 & 0 \\ \hline 8 & 0.1203 & 0.0123 & 0 \\ \hline 9 & 0.1611 & 0.0357 & 0.0002 \\ \hline 10 & 0.1783 & 0.067 & 0.0022 \\ \hline 11 & 0.1611 & 0.1212 & 0.0072 \\ \hline 12 & 0.1157 & 0.1571 & 0.0201 \\ \hline 13 & 0.0764 & 0.1896 & 0.0526 \\ \hline 14 & 0.0358 & 0.1659 & 0.1104 \\ \hline 15 & 0.0142 & 0.1306 & 0.1712 \\ \hline 16 & 0.0045 & 0.071 & 0.2155 \\ \hline 17 & 0.0011 & 0.0303 & 0.2044 \\ \hline 18 & 0 & 0.0104 & 0.1461 \\ \hline 19 & 0 & 0.0019 & 0.0587 \\ \hline 20 & 0 & 0.0001 & 0.0114 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|} \hline & \multicolumn{3}{|c|}{ Proportion of simulated samples } \\ \hline Number of people in favor of union & p=0.5 & p=0.65 & p=0.8 \\ \hline 0 & 0 & 0 & 0 \\ \hline 1 & 0 & 0 & 0 \\ \hline 2 & 0.0003 & 0 & 0 \\ \hline 3 & 0.0013 & 0.0001 & 0 \\ \hline 4 & 0.0044 & 0 & 0 \\ \hline 5 & 0.0161 & 0 & 0 \\ \hline 6 & 0.0373 & 0.0018 & 0 \\ \hline 7 & 0.0721 & 0.005 & 0 \\ \hline 8 & 0.1203 & 0.0123 & 0 \\ \hline 9 & 0.1611 & 0.0357 & 0.0002 \\ \hline 10 & 0.1783 & 0.067 & 0.0022 \\ \hline 11 & 0.1611 & 0.1212 & 0.0072 \\ \hline 12 & 0.1157 & 0.1571 & 0.0201 \\ \hline 13 & 0.0764 & 0.1896 & 0.0526 \\ \hline 14 & 0.0358 & 0.1659 & 0.1104 \\ \hline 15 & 0.0142 & 0.1306 & 0.1712 \\ \hline 16 & 0.0045 & 0.071 & 0.2155 \\ \hline 17 & 0.0011 & 0.0303 & 0.2044 \\ \hline 18 & 0 & 0.0104 & 0.1461 \\ \hline 19 & 0 & 0.0019 & 0.0587 \\ \hline 20 & 0 & 0.0001 & 0.0114 \\ \hline \end{tabular}