Can someone help with this one? Maybe.........?

laceylee

New member
Joined
Jan 17, 2013
Messages
10
Keep in mind I made this word problem as you read if you see any mistakes...I am open to constructive criticism and help!!!! Now I am at the same point on this one as I am on my last one....I am to the question of


--->Compare the observed value of the statistic to the critical value obtained for the chosen a(level of significance)

Here is the new problem I made:
A local small potato chip company has received many complaints that customers are not getting the 270g per family size bag of Big Boys Smokey Bacon Potato Chips. The owner of the company wants to make sure customers are not getting “ripped off” and are getting what they pay for in order to not lose their customer base. The owner would like to ensure this is not happening and if it is he would like this problem to be identified and looked into closely. The owner randomly chose one bag from 15 different cartons to test the weight of each of them. The owner has stated he wants to ensure the defect rate of being 5% level of significance.


  1. Null hypothesis: H0: μ ≥ 270g
Alternate hypothesis: HA: μ < 270g

  1. a= .05
Trial
Weight in Grams
1
256
2
261
3
273
4
268
5
279
6
267
7
270
8
259
9
263
10
277
11
271
12
264
13
269
14
281
15
264
Average of tested samples is: 268.13 -- Std. Dev.: 7.28
C:\DOCUME~1\SANDRA~1\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz


4. T= - μ
S/√n
268.13-270= -.99
7.28/√15

HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! :confused:
 
Keep in mind I made this word problem as you read if you see any mistakes...I am open to constructive criticism and help!!!! Now I am at the same point on this one as I am on my last one....I am to the question of


--->Compare the observed value of the statistic to the critical value obtained for the chosen a(level of significance)

Here is the new problem I made:
A local small potato chip company has received many complaints that customers are not getting the 270g per family size bag of Big Boys Smokey Bacon Potato Chips. The owner of the company wants to make sure customers are not getting “ripped off” and are getting what they pay for in order to not lose their customer base. The owner would like to ensure this is not happening and if it is he would like this problem to be identified and looked into closely. The owner randomly chose one bag from 15 different cartons to test the weight of each of them. The owner has stated he wants to ensure the defect rate of being 5% level of significance.


  1. Null hypothesis: H0: μ ≥ 270g
Alternate hypothesis: HA: μ < 270g

  1. a= .05
TrialWeight in Grams
1256
2261
3273
4268
5279
6267
7270
8259
9263
10277
11271
12264
13269
14281
15264
Average of tested samples is: 268.13 -- Std. Dev.: 7.28
C:\DOCUME~1\SANDRA~1\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz


4. T= - μ
S/√n
268.13-270= -.99
7.28/√15

HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! :confused:
Your null hypothesis does not solve the problem. It isn't the mean of the distribution that matters, but the 5% tail. The owner actually wants the probability that the mass is below 270g to be at most 5%. In your sample data, 2/3 of the bags are smaller than the mass printed on the bag, yet H0 would not be rejected. They have to raise the amount in the average bag to keep the customers from feeling cheated. You need a different H0.

Given std.dev.=7.28g, what would µ have to be so that only 5% of the distribution lies in the lower tail below 270g? The 0.05 level is at x=-1.645. You could revise H0 to be
H0: µ = 270g + 1.645×7.28g = 282g
HA: µ < 282g
The 95% confidence level again corresponds to the critical value being -1.645.

Compute the z-statistic using 282g in place of 270g.
 
I think this is where I get confused, my professor said that H0 must use the same data as HA, but have different assumptions....such as H0=μ≥282 then HA=μ<282
So this is how I should change it, correct? I had began to do so, but here is my problem, the owner wants there to be less than 5% defect under 270 so to me that doesnt make sense all too well.
 
I think this is where I get confused, my professor said that H0 must use the same data as HA, but have different assumptions....such as H0=μ≥282 then HA=μ<282
So this is how I should change it, correct? I had began to do so, but here is my problem, the owner wants there to be less than 5% defect under 270 so to me that doesnt make sense all too well.
A bag is deficient if it contains less than 270g.
If 5% are deficient, that means there is a 5% probability of being in the low tail of the distribution.
For a normal distribution, the lower 5% point is at x=-1.645; that is, 1.645 standard deviations below the mean.
The observed standard deviation (from 15 random bags) is 7.28g.
The value of 270g should be 1.645×7.28g below the mean, or the mean should be 12.0g greater than 270g.
H0 = μ ≥ 282g
HA = µ < 282g
 
A bag is deficient if it contains less than 270g.
If 5% are deficient, that means there is a 5% probability of being in the low tail of the distribution.
For a normal distribution, the lower 5% point is at x=-1.645; that is, 1.645 standard deviations below the mean.
The observed standard deviation (from 15 random bags) is 7.28g.
The value of 270g should be 1.645×7.28g below the mean, or the mean should be 12.0g greater than 270g.
H0 = μ ≥ 282g
HA = µ < 282g

Thank you! I figured it out!!!!! yay!!!! :p I saw where I was going wrong, I appreciate it very much!!!! :D
 
Top