To what extent do syntax textbooks, which analyze the structure of sentences, il

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(juvenile)

Female    60    49

Male 133 52

(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.)

p?F =

SEF =

p?M =

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 p?F ? p?M. Round your value for z to two decimal places and round your P-value to four decimal places.) z =

P-value =

Explanation / Answer

a)
For females

p = 49/60 = 0.8167

standard error = sqrt(p *(1-p)/n)
= sqrt(0.8167 * (1-0.8167)/60)
= 0.050

For males

p = 52/133 = 0.391

standard error = sqrt( p *(1-p)/n)
= sqrt(0.391 * (1-0.391)/133)
= 0.042

b)

z value at 90% = 1.645

CI = (p1 - p2) +/- z * sqrt( p1 * (1-p1)/n1 + p2 *(1-p2)/n2)
= ( 0.817 - 0.391) +/- 1.645 * sqrt((0.8167 * (1-0.8167)/60) + 0.391 * (1-0.391)/133))

= (0.318,0.534)

c)

Hypothesis:
H0 : p1 = p2
Ha : p1 not equals to p2

Test statistics:

p = (p1 * n1 + p2 * n2) / (n1 + n2)
= ( 0.817 * 60 + 0.391 * 133) / ( 60+133)
= 0.5234

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
= sqrt( 0.5234 * (1-0.5234) * ((1/60) + ( 1/133)))
= 0.0777

z = (p1 - p2) / SE
= ( 0.817 - 0.391) / 0.0777
= 5.48

P VALUE = 0.00001

Reject The null hypothesis

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