A school administrator claims that students whose first language learned is NOT English score worse on the verbal portion of the SAT exam than students whose first language learned is English. The mean SAT score of students whose first language is English is 516 (on the basis of information obtained from the College Board). Suppose a SRS of 20 students whose first language is NOT English results in a sample mean verbal score of 458. Is this evidence that the researcher's claim is true?

Question

Payton Higgins

Mathematics

11 August, 05:18

A school administrator claims that students whose first language learned is NOT English score worse on the verbal portion of the SAT exam than students whose first language learned is English. The mean SAT score of students whose first language is English is 516 (on the basis of information obtained from the College Board). Suppose a SRS of 20 students whose first language is NOT English results in a sample mean verbal score of 458. Is this evidence that the researcher's claim is true?

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Meyer · Answer 1

Xbar = 458

TS = (xbar - mu) / (sd/sqrt (N))

= (458 - 515) / (112/sqrt (20))

= - 2.27599

p-value = P (Z < - 2.27599)

= 0.0114

we reject the null hypothesis at 5 % level of significance

and fail to reject the null at 1 %

a type I error is the incorrect rejection of a true null hypothesis (also known as a "false positive" finding), while a type II error is incorrectly retaining a false null hypothesis

type i error - we conclude that SAT Verbal Score will be lower than those students whose first language is English, even though when it is not true

type ii error - we fail to conclude that SAT Verbal Score will be lower than those students whose first language is English, when it is infact true

type i error is more serious