Assignment 9 Fa 2023

POLS 3316. Statistics for Political Science Dr. Scott Basinger Homework Assignment #9 Distributed Thursday, November 9, 2023 Due Thursday, November 16, 2023 Name A survey conducted in 2006 asked 1,000 adult Americans to name one justice who is currently serving on the United States Supreme Court. 430 respondents could name at least one justice. 1. The proportion of people in the sample who could name at least one Supreme Court justice equals _____ = 𝑝𝑝̂ . 2. Fill in the table below: Standard error of 𝑝𝑝̂ Margin of error = 1.96 x standard error… 3. The 95% confidence interval for the proportion of the population who can name at least one Supreme Court justice is between ______ and ______. A recent survey asked parents whether they agreed with a series of controversial statements. One such statement was, “Homework should be banned.” Out of 1,545 respondents, 250 parents answered yes. 4. The proportion of respondents in the sample who believe homework should be banned equals _____ = 𝑝𝑝̂ . 5. Fill in the table below: Standard error of 𝑝𝑝̂ Margin of error = 1.96 x standard error… 6. The 95% confidence interval for the proportion of parents in the population who believe homework should be banned is between ______ and ______. The Public Religion Research Institute conducted a survey of 1,013 U.S. adults between January 18 – 22, 2017. Respondents were asked to agree or disagree with the statement, “God rewards athletes who have faith with good health and success.” 38 respondents refused to answer the question or said “don’t know.” Of the 975 who responded, ⋅ 499 respondents agreed (179 completely agreed ; 320 mostly agreed ) ⋅ 476 respondents disagreed (192 mostly disagreed ; 284 completely disagreed ) 7. The proportion of respondents in the sample who agreed ( completely agree + mostly agree ) is _____ = 𝑝𝑝̂ . 8. Fill in the table below: Standard error of 𝑝𝑝̂ Margin of error = 1.96 x standard error… 9. The 95% confidence interval for the proportion of the population who agree that God rewards athletes who have faith with good health and success is between ______ and ______.

The 2014 General Social Survey asked respondents to agree or disagree with the following statement, “It is much better for everyone involved if the man is the achiever outside the home and the woman takes care of the home and the family.” Out of 1,655 respondents, 515 agreed and 1,140 disagreed. 10. The proportion of respondents in the sample who agreed with the statement equals _____ = 𝑝𝑝̂ . 11. Fill in this table: Standard error of 𝑝𝑝̂ Margin of error = 1.96 x standard error… 12. The 95% confidence interval for the proportion of the population who believe that only men should be the achievers outside the home is between ______ and ______. Is there a gender divide? The sample consisted of 745 men and 910 women. 13. Of the 745 men, 247 agreed with the statement and 498 disagreed. The proportion of men in the sample who believe that only men should be the achievers outside the home is _____ = 𝑝𝑝̂ M 14. Fill in this table: Standard error of men sample proportion ( 𝑝𝑝̂ M ) Margin of error = 1.96 x standard error… 15. The 95% confidence interval for the proportion of men in the population who believe only men should be the achievers outside the home is between _______ and _______. 16. Of the 910 women, 268 agreed with the statement and 642 disagreed. The proportion of women in the sample who believe that only men should be the achievers outside the home is _____ = 𝑝𝑝̂ W 17. Fill in this table: Standard error of women sample proportion ( 𝑝𝑝̂ W ) Margin of error = z * x standard error… 18. The 95% confidence interval for the proportion of women in the population who only men should be the achievers outside the home is between _______ and _______. 19. Fill in this table to show every step necessary to perform a difference-of-proportions test of the null hypothesis that equal proportions of men and women agree with the statement (i.e., π M – π W = 0). Difference of proportions 𝑝𝑝̂ M – 𝑝𝑝̂ W = Standard error of difference of proportions z statistic 20. Performing a z test would lead you to re _ _ _ _ _ the null hypothesis of no difference.

Some useful equations: Sample proportion ( 𝑥𝑥 satisfy some condition among 𝑛𝑛 respondents or cases) 𝑝𝑝̂ = 𝑥𝑥 𝑛𝑛 Standard error of a sample proportion 𝑆𝑆 𝑝𝑝� = � 𝑝𝑝̂ (1 − 𝑝𝑝̂ ) 𝑛𝑛 Margin of error for a sample proportion 𝑚𝑚 = 𝑧𝑧 ∗ 𝑆𝑆 𝑝𝑝� = 𝑧𝑧 ∗ � 𝑝𝑝̂ (1 − 𝑝𝑝̂ ) 𝑛𝑛 Confidence interval for a sample proportion 𝑝𝑝̂ ± 𝑚𝑚 = 𝑝𝑝̂ ± 𝑧𝑧 ∗ � 𝑝𝑝̂ (1 − 𝑝𝑝̂ ) 𝑛𝑛 One-sample z statistic for a proportion against a null hypothesis about the population proportion ( 𝜋𝜋 0 ) 𝑧𝑧 = 𝑝𝑝̂ − 𝜋𝜋 0 � 𝑝𝑝̂ (1 − 𝑝𝑝̂ ) 𝑛𝑛 Difference of proportions (between samples) 𝐷𝐷 � = 𝑝𝑝 2 � − 𝑝𝑝 1 � Standard error of difference of proportions for confidence interval for the difference between population proportions ( 𝜋𝜋 2 − 𝜋𝜋 1 ) 𝑆𝑆 𝐷𝐷 � ≡ 𝑆𝑆 𝑝𝑝 2 �−𝑝𝑝 1 � = � 𝑝𝑝 1 � (1 − 𝑝𝑝 1 � ) 𝑛𝑛 1 + 𝑝𝑝 2 � (1 − 𝑝𝑝 2 � ) 𝑛𝑛 2 Confidence interval for the difference of population proportions 𝐷𝐷 � ± 𝑧𝑧 ∗ 𝑆𝑆 𝐷𝐷 � Standard error of difference of proportions for difference-of-proportions test 𝑆𝑆 𝐷𝐷 � 𝑝𝑝 ≡ 𝑆𝑆 𝑝𝑝 2 �−𝑝𝑝 1 � = � 𝑝𝑝̂ (1 − 𝑝𝑝̂ ) 𝑛𝑛 1 + 𝑝𝑝̂ (1 − 𝑝𝑝̂ ) 𝑛𝑛 2 Two-sample z statistic for a difference of proportions test (against a null hypothesis of no difference, i.e., 𝜋𝜋 1 = 𝜋𝜋 2 ) 𝑧𝑧 = 𝐷𝐷 � 𝑆𝑆 𝐷𝐷 � 𝑝𝑝