Part 1When President Donald Trump took office, he believed that the reason he did not win the popular vote was because 3 to 5 million people voted illegally. Explain how hypothesis testing might be used in a similar fashion as the legal analogy example. Part 1Choose the correct choice below. A. The null hypothesis is President Trump's belief that no voter fraud had occurred. The alternative hypothesis is that voter fraud had occurred. If we cannot prove the alternative hypothesis, then his belief will remain, but it hasn't been proven, even with the lack of contradictory evidence. B. The null hypothesis is President Trump's belief that voter fraud had occurred. The alternative hypothesis is that no voter fraud had occurred. If we can prove the null hypothesis, then his belief will remain, but it hasn't been proven, even with the lack of contradictory evidence. C. The null hypothesis is President Trump's belief that no voter fraud had occurred. The alternative hypothesis is that voter fraud had occurred. If we can prove the null hypothesis, then his belief will remain, but it hasn't been proven, even with the lack of contradictory evidence. D. The null hypothesis is President Trump's belief that voter fraud had occurred. The alternative hypothesis is that no voter fraud had occurred. If we cannot prove the alternative hypothesis, then his belief will remain, but it hasn't been proven, even with the lack of contradictory evidence.

Question

Part 1When President Donald Trump took​ office, he believed that the reason he did not win the popular vote was because 3 to 5 million people voted illegally. Explain how hypothesis testing might be used in a similar fashion as the legal analogy example. Part 1Choose the correct choice below. A. The null hypothesis is President​ Trump's belief that no voter fraud had occurred. The alternative hypothesis is that voter fraud had occurred. If we cannot prove the alternative​ hypothesis, then his belief will​ remain, but it​ hasn't been​ proven, even with the lack of contradictory evidence. B. The null hypothesis is President​ Trump's belief that voter fraud had occurred. The alternative hypothesis is that no voter fraud had occurred. If we can prove the null​ hypothesis, then his belief will​ remain, but it​ hasn't been​ proven, even with the lack of contradictory evidence. C. The null hypothesis is President​ Trump's belief that no voter fraud had occurred. The alternative hypothesis is that voter fraud had occurred. If we can prove the null​ hypothesis, then his belief will​ remain, but it​ hasn't been​ proven, even with the lack of contradictory evidence. D. The null hypothesis is President​ Trump's belief that voter fraud had occurred. The alternative hypothesis is that no voter fraud had occurred. If we cannot prove the alternative​ hypothesis, then his belief will​ remain, but it​ hasn't been​ proven, even with the lack of contradictory evidence.

BlackTom AI · Accepted Answer

1. Relevant knowledge points and concepts
The null hypothesis (H0) represents the presumption or status quo; the alternative hypothesis (H1) represents the claim to be proven. Statistical hypothesis testing evaluates evidence against H0. A failure to reject H0 does not prove H0 true; rejecting H0 provides evidence for H1. Burden of proof rests on providing sufficient evidence to reject H0 (analogous to “beyond reasonable doubt” in a trial).

2. Complete reasoning process step by step
- Translate the statements into hypotheses: the default (no illegal votes) is H0; the claim of 3–5 million illegal votes is H1.
- Formally: H0: no voter fraud (or fraud = 0 / no systematic fraud); H1: voter fraud occurred (fraud > 0).
- Choose a significance level (α), collect sample data (ballots, records), compute an appropriate test statistic, and find the p-value.
- Decision rule: if p-value ≤ α, reject H0 and accept that there is sufficient evidence for H1 (voter fraud). If p-value > α, fail to reject H0 — insufficient evidence to support H1.

3. Intermediate (symbolic) steps for a test
- Define parameter (e.g., proportion p of illegal votes). H0: p = 0 (or p ≤ threshold); H1: p > 0 (or p > threshold).
- Calculate sample statistic p̂, compute z = (p̂ − p0) / sqrt(p0(1−p0)/n), find p-value.
- Compare p-value to α, make decision as above.

4. Why the correct answer is correct
Answer A correctly sets H0 as the presumption of no fraud and H1 as the claim of fraud. It correctly states that if we cannot prove the alternative (i.e., do not reject H0), the presumption remains but is not proven—matching the logic of hypothesis testing.

5. Why the other options are incorrect
- B and D incorrectly make H0 the claim of fraud; that reverses the presumption and burden of proof. H0 should be the status quo.
- C correctly sets H0/H1 like A but then wrongly asserts “If we can prove the null hypothesis…” — we generally cannot prove H0 true; we only fail to reject it.

6. Conclusion and confirmation
Therefore the best choice is A. This matches the provided correct answer: A.

类似问题

Historically, the mean systolic blood pressure (SBP) has been a rather high value for adults in the population. We are interested in whether a recent health campaign on diet and exercise has potentially lowered the mean. Which are the correct hypotheses?

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