46815.26 points Previous Arnavers Mrtrostata To what extent do syntax textbooks,

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46815.26 points Previous Arnavers Mrtrostata To what extent do syntax textbooks, which analyze the structure of sentences, lustrate gender blas? 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 iuvenile (girl) equal to the proportion of male references are juvenile (boy)? Here are data from one of the texts: 130 (a) Find the proportion of juvenile references for females and its standard error. Do the same for the males (Round answers to three decimal places.) AM- 0408 SEM- 0043 b) Give a go confidence interval for not use rounded values, Round your final answers three decinalplaces.) the difference. (Do to 0281 0503 (c) use a test of significance to examine whether the two proportions are equaL (use A p Round your value for tto two dedmal placom and round your p value to four dedma places 503 p-value -0000 State your conclusion. There is sufficient evidence to conclude that the two proportions are o There is not sufficient evidence to conclude that the two proportions are dnerent

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P1 = P2

Alternative hypothesis: P1 P2

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the proportion from population 1 is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.

Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).

p = (p1 * n1 + p2 * n2) / (n1 + n2)

p = 0.532

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

SE = 0.07791

z = (p1 - p2) / SE

z = 5.04

where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.

Since we have a two-tailed test, the P-value is the probability that the z-score is less than - 5.04 or greater than 5.04.

Thus, the P-value = less than 0.00001

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we cannot accept the null hypothesis.

There is sufficient evidence to conclude that two proportion are different.

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