Finding Standard Deviation

#1
Hello everyone. I am new here, so excuse me if I sound a little too noobish. I am currently faced with the current problem on my homework. It isn't urgent, but finals are coming up and this is one thing I'm really struggling with.

Johnson Electronics makes calculators. Consumer satisfaction is one of the top priorities of the company's management. The company guarantees the refund of money or a replacement for any calculator that malfunctions within two years from the data of purchase. It is known from past data that despite all efforts, 5% of the calculators manufactured by this company malfunction within a 2-year period. The company recently mailed 500 such calculators to its customers.

Find the probability that exactly 29 of the 500 calculators will be returned for refund or replacement within a 2-year period.

So from the given, I have concluded:
h0:u=.05, h1:u>.05 (Not positive these are right)
n=500, xbar=.058

I cannot determine the value of the standard deviation (will be referred to as s).

The formula I believe I need to use for this equation is:
Z=(xbar-u0)/(s/sqrt(n))
Then using the chart, figure out what the P value is.

I will attempt to elaborate further upon request.

Thank you in advance!
Kroger
 

trinker

ggplot2orBust
#2
h0:u=.05, h1:u>.05 (Not positive these are right)
Null (H0's) hypotheses are not written in terms of alpha.

The formula I believe I need to use for this equation is:
Z=(xbar-u0)/(s/sqrt(n))
Then using the chart, figure out what the P value is.
This sounds pretty good to me. Go ahead and do it and let us know what you get.
 
#3
Null (H0's) hypotheses are not written in terms of alpha.



This sounds pretty good to me. Go ahead and do it and let us know what you get.
I was referring the .05 being the 5% in the stated problem.
For the equation I have, I cannot figure out how to determine what the standard deviation is. This is where I am stuck.
 

Dason

Ambassador to the humans
#4
Null (H0's) hypotheses are not written in terms of alpha.
I'm thinking that their 5% is coming from the failure percentage of the population actually.

My main concern with that is that it seems like this is a test of proportion and not a test of the mean (although really it's the same thing sometimes people can get hung up on those small details).
 

BGM

TS Contributor
#6
Not sure how this question is related to hypothesis testing. I think it is just a simple question asking the probability related to a Binomial distribution.
 
#7
Not sure how this question is related to hypothesis testing. I think it is just a simple question asking the probability related to a Binomial distribution.
So I am actually way off cue here? Not to try to get pity or anything, but I missed like 5 classes (mainly covering this chapter) due to the death of my grandmother. So I am way behind and very confused.
 

trinker

ggplot2orBust
#8
I see your problem: [TEX]{S}=\sqrt{\frac{\sum(x_i-\bar{x})^2}{n}}[/TEX]

This is because you're comparing two proportions. Different formula.

EDIT: I see Dason has already given you that clue.
 

Dason

Ambassador to the humans
#10
EDIT: I see Dason has already given you that clue.[/COLOR]
If I did it was an accident. I didn't really read the original post thoroughly. It was more of a comment that typically we would frame the hypothesis in terms of the population. But really reading over the problem I don't really think there should be a hypothesis test at all - which is what BGM is hinting at.
 

Dason

Ambassador to the humans
#13
Mainly because it seems that the actual question is just:
Find the probability that exactly 29 of the 500 calculators will be returned for refund or replacement within a 2-year period.
 

trinker

ggplot2orBust
#14
dason said:
If I did it was an accident. I didn't really read the original post thoroughly. It was more of a comment that typically we would frame the hypothesis in terms of the population. But really reading over the problem I don't really think there should be a hypothesis test at all - which is what BGM is hinting at.
yeah: (TS requires I have a certain number of characters to post)

Dason said:
My main concern with that is that it seems like this is a test of proportion and not a test of the mean (although really it's the same thing sometimes people can get hung up on those small details)
 
#15
So with my current Z formula:
(.058-.05)/(.00036/sqrt(500))= 496.90

That does not seem right haha.


EDIT: Just saw your edit, I will check that link out and then attempt to solve my question and reword if necessary.
 

trinker

ggplot2orBust
#16
Still smells like a hypothesis test to me.

And I take back my comment of:

trinker said:
Null (H0's) hypotheses are not written in terms of alpha.
I did not read carefully this was P not a pvalue.
 

trinker

ggplot2orBust
#17
PhatKroger10 please listen to BMG and Dason they're both more knowledgeable than I am. I'd wait to see what they have to say.
 
#18
If it is of any help, here is the hint given to me following my first failed attempt.

"The number of calculators returned for refund or replacement is a random variable with a binomial distribution. Find mean and standard deviation."
 

Dason

Ambassador to the humans
#19
It is a binomial probability calculation like we mentioned before. I think why they want you to get the mean and standard deviation is that your calculator probably can't handle the numbers required to do an exact binomial calculations so you'll probably need to do a normal approximation.
 
#20
It is a binomial probability calculation like we mentioned before. I think why they want you to get the mean and standard deviation is that your calculator probably can't handle the numbers required to do an exact binomial calculations so you'll probably need to do a normal approximation.
I don't believe it mentions mean anywhere in the problem. I will look up how to do a binomial calculation on my TI-83+ and inform you of the results.