Question

In: Statistics and Probability

For reasons known only to social scientists, the General Social Survey (GSS) regularly asks its subjects...

For reasons known only to social scientists, the General Social Survey (GSS) regularly asks its subjects their astrological sign. Here are the counts of responses for the 2012 GSS:

sign Aries Taurus Gemini Cancer Leo Virgo
count 145 167 170 158 185 158
sign Libra Scorpio Sagittarius Capricorn Aquarius Pisces
count 187 139 146 147 161 164

If births are spread uniformly across the year, we expect all 12 signs to be equally likely. Are they? Use α=0.05. χ2(±0.0001)= ________

P(±0.0001)=__________

a) There is evidence that all 12 signs are not equally likely.

b) There is no evidence that all 12 signs are not equally likely

Solutions

Expert Solution

The total number of persons is: 1927

If all the signs are equally likely then expected count in each category is

E = 1927 / 12 = 160.5833

Test statistic is

O: Observed frequency
E: Expected frequency.

O E (O-E) (O-E)^2 (O-E)^2/E
145 160.5833 -15.5833 242.8403 1.512238
167 160.5833 6.416667 41.17361 0.2564
170 160.5833 9.416667 88.67361 0.552197
158 160.5833 -2.58333 6.673611 0.041559
185 160.5833 24.41667 596.1736 3.71255
158 160.5833 -2.58333 6.673611 0.041559
187 160.5833 26.41667 697.8403 4.345658
139 160.5833 -21.5833 465.8403 2.900925
146 160.5833 -14.5833 212.6736 1.324382
147 160.5833 -13.5833 184.5069 1.148979
161 160.5833 0.416667 0.173611 0.001081
164 160.5833 3.416667 11.67361 0.072695
Total 1927 15.91

Degrees of freedom = Number of E's - 1 = 12 - 1 = 11

The p-value of the test: 0.1445

Since the p-value is greater than α=0.05 so we fail to reject the null hypothesis.

There is no evidence that all 12 signs are not equally likely.


Related Solutions

QUESTION 1: For reasons known only to social scientists, the General Social Survey (GSS) regularly asks...
QUESTION 1: For reasons known only to social scientists, the General Social Survey (GSS) regularly asks its subjects their astrological sign. Here are the counts of responses for the 2012 GSS: Sign Aries Taurus Gemini Cancer Leo Virgo Count 142 155 160 156 187 169 Sign Libra Scorpio Sagittarius Capricorn Aquarius Pisces Count 188 152 155 142 166 150 If births are spread uniformly across the year, we expect all 12 signs to be equally likely. Are they? Use α=0.05α=0.05....
The general social survey (GSS) is a yearly survey of adult US citizens on a variety...
The general social survey (GSS) is a yearly survey of adult US citizens on a variety of social issues. Over 5300 different questions have been asked over the nearly 40 years of administering the survey, with many of the questions, the same from year to year. Here are some of the questions asked: i. Gender (Male/Female) ii. Age (years) iii. Highest Degree Earned (None, High School Diploma, Associate’s level, Bachelor’s level, Post-bachelor’s [MS, PhD, MD, etc.]) iv. Political Party (Republican,...
what is General Social Survey (GSS), and why is it such an important source of data...
what is General Social Survey (GSS), and why is it such an important source of data for understanding American society? Write a brief paragraph that describes the GSS.
. (25.09) The University of Chicago's General Social Survey (GSS) is the nation’s most important social...
. (25.09) The University of Chicago's General Social Survey (GSS) is the nation’s most important social science sample survey. The GSS asked a random sample of adults their opinion about whether astrology is very scientific, sort of scientific, or not at all scientific. Here is a two-way table of counts for people in the sample who had three levels of higher education degrees: Degree Held Junior College Bachelor Graduate Not at all scientific 42 122 73 Very or sort of...
QUESTION 1: The University of Chicago's General Social Survey (GSS) is the nation’s most important social...
QUESTION 1: The University of Chicago's General Social Survey (GSS) is the nation’s most important social science sample survey. The GSS asked a random sample of adults their opinion about whether astrology is very scientific, sort of scientific, or not at all scientific. Here is a two-way table of counts for people in the sample who had three levels of higher education degrees: Degree Held Junior College Bachelor Graduate Not at all scientific 45 124 71 Very or sort of...
Respondents in the 2017 General Social Survey (GSS) were asked “on an average work day, about...
Respondents in the 2017 General Social Survey (GSS) were asked “on an average work day, about how many hours do you have to relax or pursue the activities that you enjoy?”. 244 males responded to the question and 262 females responded. Men reported an average of 3.28 hours per day (with a standard deviation of 2.12 hours) and women reported an average of 2.99 hours per day (sd=2.05). A. Calculate and interpret the 95% confidence interval for relaxation hours for...
According to data from the 2018 General Social Survey (GSS 2018), the average number of years...
According to data from the 2018 General Social Survey (GSS 2018), the average number of years of education of the 2345 adults in the U.S. sample is 13.73, with a standard deviation of 2.974. Compared to the national average of 13.26 years of education in 2000, researchers are wondering if the national education level had increased during these years. Do a hypothesis testing with α=0.05. Use this example to answer questions 24 to 27. 24. What’s the null hypothesis in...
use the data collected from the 2012 General Social Survey (GSS) in which 1,298 respondents reported...
use the data collected from the 2012 General Social Survey (GSS) in which 1,298 respondents reported on the number of hours they watched tv per day. The results show that the average (mean) number of hours spent watching tv per day is 3.089 hours with a standard deviation of 2.87 hours. 3.) Calculate a 95% confidence interval to estimate the mean number of hours of tv the average American watches per day. Interpret this in English. what does this mean?
Political parties want to know what groups of people support them. The General Social Survey (GSS)...
Political parties want to know what groups of people support them. The General Social Survey (GSS) asked its 2014 sample, "Generally speaking, do you usually think of yourself as a Republican, Democrat, Independent, or what?" The GSS is essentially an SRS of American adults. Here is a large two-way tale breaking down the responses by the highest degree the subject held: None High School Junior High Bachelor Graduate Strong Democrat 53 198 23 81 64 Not strong Democrat 52 204...
Political parties want to know what groups of people support them. The General Social Survey (GSS)...
Political parties want to know what groups of people support them. The General Social Survey (GSS) asked its 2014 sample, "Generally speaking, do you usually think of yourself as a Republican, Democrat, Independent, or what?" The GSS is essentially an SRS of American adults. Here is a large two-way tale breaking down the responses by the highest degree the subject held: None High School Junior College Bachelor Graduate Strong Democrat 53 198 23 81 64 Not strong Democrat 52 204...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT