A school administrator claims that students whose first language learned is not

Question

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 is English. The mean SAT verbal score of students whose first language is English is 515 with a population standard deviation of 112, on the basis of data obtained from the College board. SAT verbal scores are normally distributed. In a random sample of 20 students whose first language learned was not English results in a sample mean SAT verbal score of 458.

A. Is there significant evidence in the administrator's claim that the SAT Verbal Score will be lower than those students whose first language is English? Provide statistical evidence to support your answer. Base it on the 5% level of significance and 1% level of significance. Then, based on this work, describe what the Type I and Type II errors are and the consequences of each, i.e. which one is more serious? What should be administrator do if he wants to start a new program to assist these types of students in improving their SAT scores based on the Type I and Type II errors?

Explanation / Answer

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 erro - 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

Please rate

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.