Questions 1-4: Rates of diagnosed autism among children have reached worrisome proportions. Many are concerned about what might be causing this increase. Read and answer the following questions carefully.

1.)Some observers have noted that autism rates have risen in tandem with the rates of vaccination of children against various ailments. Is this compelling evidence of a causal link between autism and vaccination? Yes or No---why or why not? Go through all four causal hurdles, showing your work, to justify your answer. (explain in 4-10 sentences, write clear).

2.)A pair of researchers recently decided to explore the question more carefully by examining a pair of adjacent counties in California, chosen such that they had similar political and racial profiles. Both counties began with the same level of autism in the late 1980's. However, the researchers found that as vaccination over time came more widespread in one county, the autism rate was also much higher in that county compared to the adjacent county, where there were fewer vaccinations. Is this an observational study, experimental study, or natural experiment? And Why? (explain in 4-10 sentences, write clear).

3.)Does this study (from the previous prompt in question 6) provide the information necessary to warrant making a causal inference? Why or Why not? (It isn't necessary to redo the causal hurdles, explain in 4-10 sentences, write clear).

4.)Suppose you are tasked to investigate the relationship between vaccinations and autism. Specify a research design that you think would provide the most valid causal inference. Justify your response with how the design overcomes the four hurdles. Be sure to discuss any practical or ethical issues in carrying out your proposed design. (explain in 4-10 sentences, write clear).

Helpful Advice(if needed): please stick to one-tailed (e.g. 0.05 column for 95% significance level) for chi-squared tests, and two-tailed (e.g. 0.025 columns for 95% significance level) for all other tests using the t-distribution, including calculating the confidence intervals for the coefficients. Also, notice that calculating confidence intervals for the sample mean using the normal distribution is slightly different from calculating confidence intervals for the coefficients using the t-distribution.