23. 0.13/0.69 points I Previous Answers MintroStat8 8.E.071. My Notes Ask Your T

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23. 0.13/0.69 points I Previous Answers MintroStat8 8.E.071. My Notes Ask Your Teacher 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 Xijuvenile) Female 62 49 Male 131 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.) SE 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 PE-pM. Round your value for z to two decimal places and round your P-value to four decimal places.) P-value

Explanation / Answer

a) pf = 49/62 = 0.790
SEf = sqrt(pf*(1-pf)/nf) = 0.052
pm = 54/131 = 0.412
SEm = sqrt(pm*(1-pm)/nm) = 0.043

b) SE = sqrt(sef2 + sem2) = 0.06724847
For 90%CI zcrit = +/-1.645
90%CI = 49/62 - 54/131 +/-1.645*0.06724847 = (0.268, 0.489)

c) H0: Pf = Pm
Ha: Pf Pm

Pooled sample proportion.p = (p1 * n1 + p2 * n2) / (n1 + n2) = 0.533679
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] } = 0.0796901
z = (pf - pm)/SE = 4.74
p = 0

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