Question 1205518


Using the formula for the standard deviation of a sampling distribution, 

desired standard error={{{sigma/sqrt(n )}}}

standard error = standard deviation of sampling distribution {{{s}}}

{{{s=sigma/sqrt(n )}}}

where {{{sigma}}} is the population standard deviation, and {{{n}}} is sample size


given that mean is {{{mu= 0.9}}}, standard deviation {{{sigma=0.2}}}, {{{s=0.01}}}, and we need to find


(a) What sample size is needed so that the standard deviation of the sampling distribution is 0.01 grams per mile ?


{{{s=sigma/sqrt(n )}}}

 {{{0.01=0.2/sqrt(n )}}}

{{{n = (0.2 / 0.01)^2 }}}

{{{n= 400}}}

so, you would need a sample size of {{{400}}} to ensure the standard deviation of the sampling distribution is {{{0.01}}} grams per mile


(b) If a smaller sample is considered, the standard deviation for  {{{x_bar}}} would be ?

 {{{x_bar=sigma/(n^0.5)}}}
 {{{x_bar=0.2/(400^0.5)}}}
 {{{x_bar=0.01}}} => THE SAME