what does it mean to interpret an answer in terms of sampling error??

Question

anonymous · Answer

the question is.... determine the percentage of sample size 4 that have mean finishing times within 5 minuites of the population mean finishing time of 61 minutes. Interpret answer in terms of sampling error

anonymous · Answer

so i go 61+- 5 to find interval of 56<x<66 minutes...
P(56-61/9/2)= -1.11=.1335
p(66-61/9/2)=1.11= .8665
.8665-.1335=.7330

but in??? terms of sampling error???

amistre64 · Answer

do you know what a confidence interval is?

amistre64 · Answer

$$p\pm E$$

amistre64 · Answer

$$E=z_\%\sqrt{\frac{\sigma^2}{n}}$$
another way to approach sigma^2 is p(1-p), or .25 if p is unknown

anonymous · Answer

so should it just be 73.3%+- 3.2985%                         ??? 

or does expressing in in terms of sampling error change my percentage? i don't see how it should.... but it IS stat...

anonymous · Answer

i think maybe what is confusing me is that we are determining a percentage... and the point estimate is in minutes....

and if i used my mu as the point estimate p i would get 
61+-3.2985 which would give me the interval +-5minutes.... but that is not a percentage

amistre64 · Answer

whats bothering me is that there is no standard deviation to speak of.  Which i spose would amount to .25, or range/4

maybe im thinking about this in the wrong way.  could it be as simple as the difference of 5, divided by the mean?

anonymous · Answer

Lol.... nope I figured it out and wanted to share.... interpreting in terms of sampling error is to say:  there is a 73.3 %chance that the true mean finishing time was within 5minutes of 61 minutes....