Question

A hypothesis test is to be performed with a Null hypothesis H_o: µ ≤ 20 and an alternative hypothesis H₁: µ > 20,  the population standard deviation is σ=3.0, the sample size is; n=30, and the significance level is α=0.025.

1) what is a type l error?

a. reject h0 when h0 is incorrect

b. reject h0 when h0 is correct

c. do not reject h0 when h0 is incorrect

d. do not reject h0 when h0 is correct

2) What is the chance of making a type I error in the above test?

a. 0.050

b. 0.0250

c. 0.0125

d. 0.1000

3. What is a type ll error?

a. reject h0 when h0 is incorrect

b. reject h0 when h0 is correct

c. do not reject h0 when h0 is incorrect

d. do not reject h0 when h0 is correct

4.  What value would the sample mean have to be greater than to reject Ho? (answer must be 3dp)

5.  It is unknown to the technician making the test, but the real value of µ=22.
What is the probability that a Type II error occurs?

6. In a word what will happen to the Type II error if the sample size increases to 60 and all else remains unchanged. Including the answer to question (4)

a. increase

b. decrease

Answer 1

we have to test that

we have given that

Population SD=σ=3.0, sample size =n=30, significance level = α=0.025.

1)

Type 1 error is defined as rejecting Null hypothesis while in actual null hypothesis is true.so

b. reject h0 when h0 is correct

2)

P(type 1 error) =level of significance =0.025 Hence

b. 0.0250

3)

Type 2 error is defined as fail to reject Null hypothesis while in actual alternative hypothesis is true (H0 false) Hence

c. do not reject h0 when h0 is incorrect

4)

since level of signficance =0.025 and we have population standard deviation so we will use Z test

now as test is right tailed so critical value is given by

P(Z> critical Value ) =0.025

from Z table P(Z>1.960) =0.025 so critical value =1.960

Hence we reject H0 if Z statistics >1.96 Hence

Hence we reject H0 if sample mean >21.074

5)

6)

since P(type 2 error) is given by

so as we see in equation as value of increases then numerator value increase in negative and value go towards left side tail of normal hence this probability will decrease as n increases hence

b. decrease