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?

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

Shania is correct.

Step-by-step explanation:

For a right angled triangle, given two sides and an angle, we can use the sine rule or the various trigonometry identities to solve the triangle;

a/sin A = b/sinB

and

sin (angle) = opposite side/hypotenuse

cos (angle) = adjacent side/hypotenuse

tan (angle) = opposite/ adjacent

assuming a is the opposite side of angle A and b is also opposite of angle B

Otherwise, the only way to solve a triangle given two sides only is by the use of the Pythagoras theorem.

Hence, Shania is correct.