# Maths help probability of type 2 errors

Watch
Announcements
#1
A simple question, but couldn't understand why I got the answer wrong.

A normal distribution with standard deviation 6.25 is being tested at the 5% significance level. The null hypothesis is H0: mean = 15.7 and the alternative is H1: mean < 15.7
a) State the probability of a type I error:
P(type I error) = 0.05 = 5%
b) Find the probability of a type II error if actually mean = 5.7:
To find the critical value:
X - N(15.7, 6.25^2)
using calculator: Inverse Normal: Left tail, 0.05 area, s.d = 6.25, mean = 15.7.
c.v. = 5.42

X - N(5.7, 6.25^2)
P(X> (or equal to) 5.42) = 1 - 0.518
= 0.482
Hence the probability of a type II error is 48.2%

c) Find the probability of a type II error if actually mean = 25.7
X - N (25.7, 6.25^2)
P(X> (or equal to) 5.42) = 1 - 0.9994123

= 5.8 x 10^-4

P(type II error) = 0.0588%

However, textbook says 0.588%, have I missed something or is it a simple incorrect answer in the textbook?
0
X

new posts
Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### Poll

Join the discussion

#### Do you think receiving Teacher Assessed Grades will impact your future?

I'm worried it will negatively impact me getting into university/college (174)
44.27%
I'm worried that I’m not academically prepared for the next stage in my educational journey (43)
10.94%
I'm worried it will impact my future career (32)
8.14%
I'm worried that my grades will be seen as ‘lesser’ because I didn’t take exams (83)
21.12%
I don’t think that receiving these grades will impact my future (39)
9.92%
I think that receiving these grades will affect me in another way (let us know in the discussion!) (22)
5.6%