computing limits

[rock9449]

compute limits for a sample mean Xbar=12 such that the sample mean is within those limits so that it can be considered satisfactory if xbar exceeds the upperlimnit or bewlow the lower limit action will be taken how do i compute these limits please can i get some help

[Dragan]

compute limits for a sample mean Xbar=12 such that the sample mean is within those limits so that it can be considered satisfactory if xbar exceeds the upperlimnit or bewlow the lower limit action will be taken how do i compute these limits please can i get some help

XBar + - Zcrit * StdError, where StdError=Sigma/Sqrt[N]

if Sigma is known constant and Zcrit is the critical value from the unit normal distribution, otherwise

XBar + - tcrit (df=N-1)*StdError where StdError=S/Sqrt[N]

and where S is the sample standard deviation and is used if Sigma is unknown and tcrit is the critical value from the student t-distriubution with degrees of freedom equal to N-1.

These intervals assume X~N(Mu, Sigma).

[rock9449]

XBar + - Zcrit * StdError, where StdError=Sigma/Sqrt[N]

if Sigma is known constant and Zcrit is the critical value from the unit normal distribution, otherwise

XBar + - tcrit (df=N-1)*StdError where StdError=S/Sqrt[N]

and where S is the sample standard deviation and is used if Sigma is unknown and tcrit is the critical value from the student t-distriubution with degrees of freedom equal to N-1.

These intervals assume X~N(Mu, Sigma).

i understand where the S,N came from but have where does StdError come from and how for this problem would i get the Zcrit is that using 12 to establish class boundries the 12 was provided in the problem sample mean x1 around u =12

[Dragan]

i understand where the S,N came from but have where does StdError come from and how for this problem would i get the Zcrit is that using 12 to establish class boundries the 12 was provided in the problem sample mean x1 around u =12

This is easy to do. Remember if you're using S, then you need to use tcrit.

Suppose, Xbar=12, N=10, and S=16.

Then it follows that:

StdError=16/Sqrt[10],

tcrit (N-1=9) = + - 2.262

with alpha =0.05 for a two-sided test.

Therefore,

XBar (12) + - (2.262)*(16/Sqrt[10]).

Easily done. Mkay.

[rock9449]

This is easy to do. Remember if you're using S, then you need to use tcrit.

Suppose, Xbar=12, N=10, and S=16.

Then it follows that:

StdError=16/Sqrt[10],

tcrit (N-1=9) = + - 2.262

with alpha =0.05 for a two-sided test.

Therefore,

XBar (12) + - (2.262)*(16/Sqrt[10]).

Easily done. Mkay.

not really because my s caculated is .220
my n is 30
and my xbar is 12however the limits dont seem to fit the numbers given

also the problem states such that as long as the sample mean iw within those limits so because the sample mean is 12 and when caculated i get

11.82-12.17 thus 12 falls into this range so is the answer complete in terms of caculating limits?


this problem incorates confidence intervals ***