Two different simple random samples are drawn from two different populations. The first sample consists of 30 people with 16 having a common attribute. The second sample consists of 2000 people with 1409 of them having the same common attribute. Compare the results from a hypothesis test of p, = p, (with a 0.01 significance level) and a 99% confidence interval estimate of p, -p2. O A. Hg: P1 SP2 H1: P1 #P2 O B. Ho: P1 *P2 H1: P1 = P2 OC. Ho: P1 = P2 H4: P1 > P2 OF. Ho: P1 = P2 O D. Ho: P1 2 P2 H1: P1 +P2 O E. Ho: P1 = P2 H1: P1 +P2 H1: P1

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Two different simple random samples are drawn from two different populations. The first sample consists of 30 people with 16 having a common attribute. The second sample consists of 2000 people with 1409 of them having the same common attribute. Compare the results from a hypothesis test of \( p_1 = p_2 \) (with a 0.01 significance level) and a 99% confidence interval estimate of \( p_1 - p_2 \).

**Options for Hypotheses:**

- **A.** \( H_0: p_1 \leq p_2 \)
  \( H_1: p_1 \neq p_2 \)

- **B.** \( H_0: p_1 \neq p_2 \)
  \( H_1: p_1 = p_2 \)

- **C.** \( H_0: p_1 = p_2 \)
  \( H_1: p_1 > p_2 \)

- **D.** \( H_0: p_1 \geq p_2 \)
  \( H_1: p_1 \neq p_2 \)

- **E.** \( H_0: p_1 = p_2 \)
  \( H_1: p_1 \neq p_2 \)

- **F.** \( H_0: p_1 = p_2 \)
  \( H_1: p_1 < p_2 \)

**Identify the test statistic.**

(Enter the value and round to two decimal places as needed.)

**Identify the critical value(s).**

(Enter the value(s) and round to three decimal places as needed. Use a comma to separate answers if needed.)

**Conclusions:**

1. What is the conclusion based on the hypothesis test?

   - The test statistic is _____ the critical region, so _____ the null hypothesis. There is _____ evidence to conclude that \( p_1 \neq p_2 \).

2. What is the conclusion based on the confidence interval?

   - The 99% confidence interval is \( < (p_1 - p_2) < \) _____ (Round to three decimal places as needed.)

   - Since 0 is _____ in the interval, it indicates to _____ the null hypothesis.
Transcribed Image Text:Two different simple random samples are drawn from two different populations. The first sample consists of 30 people with 16 having a common attribute. The second sample consists of 2000 people with 1409 of them having the same common attribute. Compare the results from a hypothesis test of \( p_1 = p_2 \) (with a 0.01 significance level) and a 99% confidence interval estimate of \( p_1 - p_2 \). **Options for Hypotheses:** - **A.** \( H_0: p_1 \leq p_2 \) \( H_1: p_1 \neq p_2 \) - **B.** \( H_0: p_1 \neq p_2 \) \( H_1: p_1 = p_2 \) - **C.** \( H_0: p_1 = p_2 \) \( H_1: p_1 > p_2 \) - **D.** \( H_0: p_1 \geq p_2 \) \( H_1: p_1 \neq p_2 \) - **E.** \( H_0: p_1 = p_2 \) \( H_1: p_1 \neq p_2 \) - **F.** \( H_0: p_1 = p_2 \) \( H_1: p_1 < p_2 \) **Identify the test statistic.** (Enter the value and round to two decimal places as needed.) **Identify the critical value(s).** (Enter the value(s) and round to three decimal places as needed. Use a comma to separate answers if needed.) **Conclusions:** 1. What is the conclusion based on the hypothesis test? - The test statistic is _____ the critical region, so _____ the null hypothesis. There is _____ evidence to conclude that \( p_1 \neq p_2 \). 2. What is the conclusion based on the confidence interval? - The 99% confidence interval is \( < (p_1 - p_2) < \) _____ (Round to three decimal places as needed.) - Since 0 is _____ in the interval, it indicates to _____ the null hypothesis.
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