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
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
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 58E: What is meant by the sample space of an experiment?
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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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