Question

The Graduate Record Examination (GRE) is a test required for admission to many US graduate schools. Student’s scores on the quantitative portion of the GRE follow a normal distribution with a mean of 150 and a standard deviation of 8.8. An admissions officer at a large graduate school believes the mean is less than 150. a)Determine the null and alternative hypotheses.

b)Explain what it would mean to make a Type I Error.

c)Explain what it would mean to make a Type II Error.

Answer 1

Answer with Step-by-step explanation:

Since we have given that

Mean = 150

Standard deviation = 8.8

An admissions officer at a large graduate school believes the mean is less than 150.

a)Determine the null and alternative hypotheses.

So, hypothesis :

`H_0:\mu =150\\\\H_a:\mu\\eq 150`

b)Explain what it would mean to make a Type I Error.

As we know that Type 1 error are those errors in which null hypothesis is supposed to be rejected but not get rejected.

So, here, mean is not less than 150 but in actual it is less than 150.

c)Explain what it would mean to make a Type II Error.

As we know that Type II error are those errors in which null hypothesis is not supposed to be rejected but it gets rejected.

So, mean is less than 150 but actually it is not less than 150.