Question

You have an SRS of size n = 9 from a normal distribution with sigma = 1 . You wish to test
H0: u=0 and Ha: u > 0
You decide to reject Ho 0 if x > 0 and to accept Ho otherwise.

a) Find the probability of a Type I error.
b) Describe a Type II error.

Answer 1

@Michele_Laino

Answer 2

what is H0?

Answer 3

Ho is the null

Answer 4

I'm sorry, I don't know your answer

Answer 5

do you know who to calculate probability of type I error?

Answer 6

is it the gaussian probability?

Answer 7

i dont know

Answer 8

n is the degree of freedom?

Answer 9

umm i don't know, this question is under types of error and powers, if that helps at all

Answer 10

please, wait I ask to another tutor

Answer 11

@dan815 can you help here please?

Answer 12

@sleepyjess please can you help her?

Answer 13

here*

Answer 14

@freckles can you help here, please?

Answer 15

thank you @Michele_Laino

Answer 16

thank you! Nevertheless your question is without answer

Answer 17

idk what to do :(

Answer 18

what subject are you studying at the moment?

Answer 19

ap statistics

Answer 20

what is the meaning of SRS?

Answer 21

simple random sample

Answer 22

please wait, I'm looking for your answer in my textbook

Answer 23

okay

Answer 24

I found this formula:
\[\Large \sigma = \sqrt {\frac{N}{{12}}} \]
where N is the size of your sample, and sigma is the requested error

Answer 25

so in our case n is 9 so we would do sqrt(9/12)?

Answer 26

yes!

Answer 27

ok i get 0.86602540378

Answer 28

ok! better is 0.9

Answer 29

ok so thats the answer for a?

Answer 30

yes, I think so!

Answer 31

no, please wait

Answer 32

ok

Answer 33

I think that the requested probability, is given by the subsequent formula:
\[\Large p = \frac{{\sqrt {\frac{N}{{12}}} }}{{{\sigma _0}}}\]
where: \[{{\sigma _0}}\] is your sigma,namely:
\[{{\sigma _0} = 1}\]

Answer 34

so (sqrt(9/12))/sigmao = .9/1 = .9

Answer 35

yes! sorry better is 87%

Answer 36

since we got 0.866....

Answer 37

oh okay so for a we would get .87

Answer 38

yes!

Answer 39

ok and for b do i just say a false null hypothesis can fail to be rejected

Answer 40

wait a moment, I'm reading my textbook

Answer 41

ok

Answer 42

yes! I think so, since we got this interval:
\[\Large \left( { - 0.87 \times \sqrt {27} ,\;0.87 \times \sqrt {27} } \right) = \left( { - 4.52{\sigma _0},\;4.52{\sigma _0}} \right)\]

Answer 43

the general formula which gives the amplitude of that interval is:
\[\Large {\frac{N}{{2}}{\sigma _0}}\]
@dennese13

Answer 44

so 3.5?

Answer 45

*4.5

Answer 46

yes! \[\Large {4.52{\sigma _0}}\] is also a right answer

Answer 47

wait so what would that go under

Answer 48

are you referring to the underlying theory?

Answer 49

no like would that go under b?

Answer 50

I think what you have said before, namely:
"a false null hypothesis can fail to be rejected"

Answer 51

wait so where do we putt he 4.5

Answer 52

I have provided that number, in order to show you that the probability of part A, is very high. Namely, we need of an objective criterion in order to answer to part B

Answer 53

The formulas which I provided you are from the theory. If you want I give you the title of my textbook

Answer 54

sure!

Answer 55

so for my answer I can put
a) .87
b) false null hypothesis can fail to be rejected

Answer 56

yes!
here is the title:
\[\large \begin{gathered}
{\mathbf{Data\;reduction\; and\; error \; analysis\; for \; the\; physical \; sciences}} \hfill \\\;
{\text{Authors: P}}{\text{.R}}{\text{.Bevington}}{\text{, D}}{\text{.K}}{\text{. Robinson}} \hfill \\
{\text{Publisher: McGraw - Hill}} \hfill \\
\end{gathered} \]

Answer 57

okay thank you so much!!

Answer 58

Thank you!!

Answer 59

oops.. the last word of the title, is:
\[\Large {\mathbf{sciences}}\]