Question 1201088: Please help me to solve this equation. The symbols aren't available on my keyboard that I need to show you. this is Statistics.
1. Managers at an automobile manufacturing plant would like to estimate the mean completion time of an assembly line operation, u. The managers plan to choose a random sample of completion times and estimate via the sample. Assuming that the standard deviation of the population of completion times is 10.2 minutes, what is the minimum sample size needed for the managers to be 95% confident that their estimate is within 1.7 minutes of u?
Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).
Note:
(If necessary, consult a list of formulas.)
A common format
Several types of confidence intervals for population means and population proportions have the following general format.
estimate + (critical value) (spread)
_
estimate-parameter
__________________
spread
estimate is the value of a statistic used to estimate one of the population parameter(s), spread is the standard deviation or standard error of the statistic, and critical value is a number that depends on the level of confidence and the sampling distribution of the statistic.
My work for the first part is
<10.2
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! population standard deviation is 10.2
confidence interval is 95%
margin of error is smaller than or equal to 1.7
critical z-score is plus or minus 1.9599963986.
x-score formula is z = (x - m) / s
z is the z-score
x is the sample mean
m is the population mean
(x - m) is the margin of error
s is the standard error
the high side critical z-score is 1.9599963986.
z-score formula becomes:
1.9599963986 = (x - m) / s
s is the standard error.
standard error is standard deviation divided by square root of sample size.
formula become:
1.9599963986 = 1.7 / s
solve for s to gets = 1.7 / 1.9599963986 = .8673628761.
formula for standard error is s = standard deviation / sqrt(sample size)
you get:
.8673628761 = 10.2 / sqrt(sample size)
solve for sqrt(sample size) to get:
sqrt(sample size) = 10.2 / .8673628761 = 11.75978392.
solve for sample size to get:
sample size = 11.75978392 squared = 138.2925177.
with a sample size of 138.2925177, you should get a margin of error equal to 1.7.
round sample size to the next highest integer to get 139.
with a sample size of 139, you should get a margin of error less than 1.7.
a sample size of 139 gets you a standard error of 10.2 / sqrt(139) = .8651527083.
that standard error gets you a margin of error equal to 1.695668151.
this is very close to, but less than, a margin of error of 1.7.
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