A survey was conducted of newlyweds in a country who have a spouse of a different race or ethnicity from their own. The survey included random samples of 1000 newlyweds in Ethnicity A and 1000 newlyweds in Ethnicity B. In the survey, 14% of respondents in Ethnicity A and 21% of respondents in Ethnicity B had a spouse of a different race or ethnicity from their own. At a=0.01, is there evidence to support the claim that the proportion of newlyweds in Ethnicity A who have a spouse of a different race or ethnicity from their own is less than the proportion of newlyweds in Ethnicity B that have a spouse of a different race or ethnicity from their own? Let p, represent the proportion of newlyweds in Ethnicity A who have a spouse of a different race or ethnicity from their own. Let p₂ represent the proportion of newlyweds in Ethnicity B that have a spouse of a different race or ethnicity from their own. State the null and alternative hypotheses. OA. Ho: P₁ P2 OB. Ho: P₁ SP₂ H₂: P1 P2 OC. Ho: P₁ = P2 H₂: P₁ P2 H₂: P₁ SP₂2 OD. Ho: P₁ P₂ O E. Ho: P₁

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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**Hypothesis Testing on Proportions of Newlyweds with Spouses of Different Race or Ethnicity**

**Scenario:**
A survey was conducted in a country to determine the proportion of newlyweds who have a spouse of a different race or ethnicity from their own. The survey included random samples of 1000 newlyweds in Ethnicity A and 1000 newlyweds in Ethnicity B. According to the survey:
- 14% of respondents in Ethnicity A had a spouse of a different race or ethnicity.
- 21% of respondents in Ethnicity B had a spouse of a different race or ethnicity.

At a significance level of α = 0.01, we aim to test whether the proportion of newlyweds in Ethnicity A who have a spouse of a different race or ethnicity from their own is less than the proportion of newlyweds in Ethnicity B.

**Hypotheses:**
Let \( p_1 \) represent the proportion of newlyweds in Ethnicity A who have a spouse of a different race or ethnicity from their own.
Let \( p_2 \) represent the proportion of newlyweds in Ethnicity B who have a spouse of a different race or ethnicity from their own.

**State the Null and Alternative Hypotheses:**

Options:
A. \( H_0: p_1 > p_2 \)
    \( H_a: p_1 \le p_2 \)

B. \( H_0: p_1 \le p_2 \)
    \( H_a: p_1 > p_2 \)

C. \( H_0: p_1 = p_2 \)
    \( H_a: p_1 \ne p_2 \)

D. \( H_0: p_1 \ge p_2 \)
    \( H_a: p_1 < p_2 \)

E. \( H_0: p_1 < p_2 \)
    \( H_a: p_1 \ge p_2 \)

F. \( H_0: p_1 \ne p_2 \)
    \( H_a: p_1 = p_2 \)

The correct hypotheses are:
D. \( H_0: p_1 \ge p_2 \)
     \( H_a: p_1 < p_2 \)

**Hypothesis Test Calculation:**

1. **Calculate the Standard
Transcribed Image Text:**Hypothesis Testing on Proportions of Newlyweds with Spouses of Different Race or Ethnicity** **Scenario:** A survey was conducted in a country to determine the proportion of newlyweds who have a spouse of a different race or ethnicity from their own. The survey included random samples of 1000 newlyweds in Ethnicity A and 1000 newlyweds in Ethnicity B. According to the survey: - 14% of respondents in Ethnicity A had a spouse of a different race or ethnicity. - 21% of respondents in Ethnicity B had a spouse of a different race or ethnicity. At a significance level of α = 0.01, we aim to test whether the proportion of newlyweds in Ethnicity A who have a spouse of a different race or ethnicity from their own is less than the proportion of newlyweds in Ethnicity B. **Hypotheses:** Let \( p_1 \) represent the proportion of newlyweds in Ethnicity A who have a spouse of a different race or ethnicity from their own. Let \( p_2 \) represent the proportion of newlyweds in Ethnicity B who have a spouse of a different race or ethnicity from their own. **State the Null and Alternative Hypotheses:** Options: A. \( H_0: p_1 > p_2 \) \( H_a: p_1 \le p_2 \) B. \( H_0: p_1 \le p_2 \) \( H_a: p_1 > p_2 \) C. \( H_0: p_1 = p_2 \) \( H_a: p_1 \ne p_2 \) D. \( H_0: p_1 \ge p_2 \) \( H_a: p_1 < p_2 \) E. \( H_0: p_1 < p_2 \) \( H_a: p_1 \ge p_2 \) F. \( H_0: p_1 \ne p_2 \) \( H_a: p_1 = p_2 \) The correct hypotheses are: D. \( H_0: p_1 \ge p_2 \) \( H_a: p_1 < p_2 \) **Hypothesis Test Calculation:** 1. **Calculate the Standard
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