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What’s in a Word?In a recent survey conducted by the Pew
Chapter , Problem 15AYU(choose chapter or problem)
Problem 15AYU
What’s in a Word?In a recent survey conducted by the Pew Research Center for the People&the Press, a random sample of adults 18 years of age or older living in the continental United States was asked their reaction to the word socialism. In addition, the individuals were asked to disclose which political party they most associate with. Results of the survey are given in the table
|
Democrat |
Independent |
Republican |
Positive |
220 |
144 |
62 |
Negative |
279 |
410 |
351 |
(a) Does the evidence suggest a different proportion of individuals within each political affiliation reacts positively to the word socialism? Use the α = 0.05 level of significance.
(b) Construct a conditional distribution of reaction by political party.
(c) Write a summary about the “partisan divide” regarding reaction to the word socialism.
Questions & Answers
QUESTION:
Problem 15AYU
What’s in a Word?In a recent survey conducted by the Pew Research Center for the People&the Press, a random sample of adults 18 years of age or older living in the continental United States was asked their reaction to the word socialism. In addition, the individuals were asked to disclose which political party they most associate with. Results of the survey are given in the table
|
Democrat |
Independent |
Republican |
Positive |
220 |
144 |
62 |
Negative |
279 |
410 |
351 |
(a) Does the evidence suggest a different proportion of individuals within each political affiliation reacts positively to the word socialism? Use the α = 0.05 level of significance.
(b) Construct a conditional distribution of reaction by political party.
(c) Write a summary about the “partisan divide” regarding reaction to the word socialism.
ANSWER:
Answer :
Step 1: Given the data represents,In a recent survey conducted by the Pew Research Center for the People & the Press, a random sample of adults 18 years of age or older living in the continental United States was asked their reaction to the word socialism. In addition, the individuals were asked to disclose which political party they most associate with. Results of the survey are given in the table.
Democrat |
Independent |
Republican |
Total |
|
Positive |
220 |
144 |
62 |
426 |
Negative |
279 |
410 |
351 |
1040 |
Total |
499 |
554 |
413 |
Grand total = 1466 |
- The null and alternative hypothesis are given by
: the evidence suggest a same proportion of individuals within each political affiliation reacts positively to the word.
: the evidence suggest a different proportion of individuals within each political affiliation reacts positively to the word.
Expected values can be calculated by using the formula,
Expected value = .
Expected value of 220 is given by E(220) = = 145.0027
Expected ( |
|||
220 |
145.0027 |
5624.595 |
38.78959 |
144 |
160.9849 |
288.4868 |
1.792012 |
62 |
120.0122 |
3365.415 |
28.04228 |
279 |
353.9972 |
5624.58 |
15.88877 |
410 |
393.015 |
288.4902 |
0.734044 |
351 |
292.9877 |
3365.427 |
11.48658 |
|
Consider,
= 96.728.
5.991 be the critical value for = 0.05.
= 96.728 >
= 5.991, we reject the null hypothesis.
There is sufficient evidence at the = 0.05 level of significance that a different proportion of individuals within each political affiliation reacts positively to the word capitalism.