Any sentence that contains and animate noun as a direct object and another noun

Question

Any sentence that contains and animate noun as a direct object and another noun as a second object (e.g., "Sue offered Ann a cookie.") is termed a double object dative (DOD). The connection between certain verbs and a DOD was investigated in Applied Psycolinguistics. The subjects were 10 native English speakers. After viewing pictures of a family, they were asked to write a sentence about the family using the verb "buy". Of the 10 sentences, 1 had a DOD structure. Does this provide sufficent evidence to conclude that the proportion of sentences with the verb "buy" that are DODs is less that 1/3?

Explanation / Answer

H0:Pu=1/3 (Proportion of sentence with the verb 'Buy' that are DOD is equal than 1/3)

H1:Pu<1/3 (Proportion of sentence with the verb 'Buy' that are DOD is less than 1/3)

To test the hypothesis, use 1-proportion Z test.

Z=(Ps-Pu)/sqrt[Pu(1-Pu)/N], where Ps and Pu corresponds to sample proportion and population proprtion, N is sample size.

=(1/10-1/3)/sqrt [1/3(1-1/3)/10]

=-1.57

p value is 0.058208

The p value is not less than alpha=0.05. Therefore, fail to reject null hypothesis. There is not sufficient sample evidence to cocnclude that Proportion of sentence with the verb 'Buy' that are DOD is less than 1/3.

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