Question

Null and alternative hypotheses help! :)

Answer 1

What is the null and alt. hypothesis of the mean amount of soup in a particular sized can is at least 16 ounces

Answer 2

@jim_thompson5910

Answer 3

1. H0 ≥ 16

Ha < 16

Answer 4

\(H_0 : \) mean = 16

\(H_A : \) mean >= 16

Answer 5

Null hypothesis MUST always have an "equal" sign

Answer 6

Wait why is it equal to and not greater than? It says at least 16, so it has to be 16 or more

Answer 7

think of it like this :
you're claiming the soup will be more than 16 ounces, so you need to prove it- hence it becomes Alternate hypothesis

Answer 8

And since NULL hypothesis must stick to some equality, you would assume that the mean stays fixed at 16, and conduct ur hypothesis testing

Answer 9

Hmm.. I guess that makes sense.
2. The majority of people in the 18-29 age bracket voted in the last presidential election.

Answer 10

Not 100% sure on this one because it has two numbers

Answer 11

Is that the entire question given ?
no other info provided ?

Answer 12

No other info

Answer 13

We can skip it for now :)

3. Salaries among female business analysts have a standard deviation greater than $3000.

Answer 14

No wait, lets do 2. first

Answer 15

these are easy actually

Answer 16

I just don't understand because of 18-29

Answer 17

2. The majority of people in the 18-29 age bracket voted in the last presidential election.

\(H_0\) : All people of ages between 18->100 voted at equal %
\(H_A\) : Majority of ppl between 18 to 29 have voted

Answer 18

3. Salaries among female business analysts have a standard deviation greater than $3000.

\(H_0\) : standard deviation of salaries of female business analysts = $3000
\(H_A\) : standard deviation > $3000

Answer 19

Wait, can you explain 2? o.O

Answer 20

I would like to change 2

Answer 21

2. The majority of people in the 18-29 age bracket voted in the last presidential election.

\(H_0\) : 50% of ppl between 18 to 29 have voted
\(H_A \): more than 50% ppl between 18 to 29 have voted

Answer 22

see if it makes sense now^

Answer 23

you're claiming that majority of ppl between ages 18 and 29 have voted, so the alternative hypotheises becomes > 50% of ppl between 18 and 29 years have voted

Answer 24

It's just weird because 18-29 isn't a variable but you can imagine it being

Answer 25

The type I and Type II errors associated with these claims:
According to a recent study, 50% of all American carry a variant of a gene that increases the risk of diabetes

Answer 26

Type 1 error : when innocent person gets punished
Type 2 error : when a criminal escapes

Answer 27

That.. actually helps a lot haha

Answer 28

in the present context :
Type 1 error : A person without that " bad gene" to be labelled as having that "bad gene"

Answer 29

Type 2 error : A person having that " bad gene" in real to be labelled as NOT having that "bad gene"

Answer 30

see if that looks okay

Answer 31

It does! :)

Answer 32

good :)

Answer 33

Hmm I'm looking at my classmates answers and they all have null hypotheses with H0>=16

Answer 34

H0: μ ≥ 12. Ha: μ < 12. is what they have. Are they just all doing it wrong with null and they don't know you can't have that?

Answer 35

from where 12 is coming from ?

Answer 36

lol they must have copied the answers from the same site,

Answer 37

have a look at my notes

Answer 38

The null hypothesis need not always be " ="

Answer 39

You an have a Ho vs Ha hypothesis that is composite vs composite

Answer 40

can have*

Answer 41

yes you're right ! it can have <= or >=
but it cannot have only < or >

Answer 42

but im not so much sure about allowing <= or >= into NULL, as the examples i did in my course are always dealing with "="

Answer 43

Well I have seen such examples. I had a stats class on estimation and hypothesis testing and we saw examples such as \(H_0: \theta \ge \theta_0 \text{ vs. }H_1: \theta < \theta_0\)

Answer 44

ohkay then fine !

Answer 45

I guess they are just not that common though in actual examples. We mostly derived "theoretical" results in hypothesis testing, but yeah in most examples you see it is common to see a null hypothesis testing for some parameter to be equal = to something.

Answer 46

i hope so, and i trust you more than my professor lol
I remember she saying "we cannot have an inequality in null hypothesis"..
let me pull up the video ....

Answer 47

looks the video is not public,
however here is the lecture slides :
https://d396qusza40orc.cloudfront.net/statistics/lecture_slides/unit3/u3_p3_2_hyp_test_mean.pdf

Answer 48

Hmm interesting hehe! Yeah I am looking through my notes now and we definitely had at least 4 examples with an inequality in the null hypothesis ;P

Answer 49

I don't have slides for my notes, but a quick google search revealed these notes, which also have inequalitie sin some null hypotheses: http://www.tsc.uc3m.es/~fernando/Feb16a.pdf

Answer 50

or maybe my professor is spoonfeeding us in the start, so that we get the general idea of hypothesis testing... and may cover up the details later... not sure... i have posted this question in the discussion forum , wil wait for her response :)

Answer 51

composite hypothesis testing doesnt look familiar to meh... looks we havent covered this yet