To what extent do syntax textbooks, which analyze the structure of sentences, il
ID: 3170485 • Letter: T
Question
To what extent do syntax textbooks, which analyze the structure of sentences, illustrate gender bias? A study of this question sampled sentences from 10 texts. One part of the study examined the use of the words "girl," "boy," "man," and "woman." We will call the first two words juvenile and the last two adult. Is the proportion of female references that are juvenile (girl) equal to the proportion of male references that are juvenile (boy)? Here are data from one of the texts:
Gender n X(juvenille)
Female 60 49
Male 130 54
(a) Find the proportion of juvenile references for females and its standard error. Do the same for the males.
(Round your answers to three decimal places.)
pF =
SEF =
pM =
SEM =
(b) Give a 90% confidence interval for the difference. (Do not use rounded values. Round your final answers to three decimal places.) ,
(c) Use a test of significance to examine whether the two proportions are equal. (Use pF pM. Round your value for z to two decimal places and round your P-value to four decimal places.)
z =
P-value =
Explanation / Answer
SolutionA:
sample proportion of females=p^F
=49/60=0.817
sample proportion of males=p^M
=54/130=0.415
standard error males=sqrt[0.817(1-0.817)/60]
=0.049
standard error females=sqrt[0.415(1-0.415)/130]
=0.043
Solutionb:
90% confidence interval for the difference in proportion=1.645
lower boundary for diff in pF pM. =(0.817-0.415)-1.645sqrt[0.817(1-0.817)/60+0.415(1-0.415)/130]
= 0.402- 0.1086
=0.296
upper boundary for diff in pF pM=
(0.817-0.415)+1.645sqrt[0.817(1-0.817)/60+0.415(1-0.415)/130]
= 0.402+ 0.1086
=0.5106
=0.511
We are 90% confident that the diff in proportion is
0.296 to 0.511
Solutionc:
Ho: pF pM.=0
H1:pF pM. not equal to 0
level of significance=0.05
Z statistic:
z=:pF pM-0/sqrt[pF(1-:pF )/n1+ pM(1- pM)/n2]
=0.402/0.066
=6.09
The P-Value is < 0.00001.
The result is significant at p < 0.05.
Reject Null hypothesis
There is sufficient evidence at 5% level of significance to support the claim
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