In 2006, authors Peters and Stringham examined data from the General Social Surv
ID: 2924961 • Letter: I
Question
In 2006, authors Peters and Stringham examined data from the General Social Survey (GSS), a nationally representative, repeated cross section that contains questions on employment status and salary, demographic characteristics, and alcohol consumption patterns. The survey question on alcohol asks respondents, “Do you ever have occasion to use any alcoholic beverages such as liquor, wine, or beer, or are you a total abstainer?” The data for full-time employees is presented in Table 1, below
Assume the GSS is equivalent to a simple random sample of the U.S. population.
In 2006, the federal limit for poverty was an annual income of $9800 or less. Was the rate of “poverty” the same for male drinkers as it was for male abstainers? Perform a test of statistical significance and calculate the appropriate test statistic; choose the answer that is closest to correct.
A. 0.077
B. 1.39
C. 5.16
D. 28.66
Can not be calculated from the information given
A. 0.077
B. 1.39
C. 5.16
D. 28.66
Can not be calculated from the information given
Table 1: Basic Facts About People in the Data Full-Time Workers Mean Standard Number of Females Earnings Deviation MalesEarnings Deviation Drinkers Abstainers N-3,480 $30,146 (24,023) N-2,56917216 (11,951) | N=765 | $25,432 | (20,300) | N-810 | $13,982- (10,278) |Explanation / Answer
Given that,
mean(x)=30146
standard deviation , 1 =24023
number(n1)=3480
y(mean)=13982
standard deviation, 2 =10278
number(n2)=810
null, Ho: u1 = u2
alternate, H1: 1 != u2
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
zo=30146-13982/sqrt((577104529/3480)+(105637284/810))
zo =29.7
| zo | =29.7
critical value
the value of |z | at los 0.05% is 1.96
we got |zo | =29.697 & | z | =1.96
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 29.7 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: 1 != u2
test statistic: 29.7
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0
our computed test statistic 29.7 is close to 28.66
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