statistics?
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YOU want to estimate the mean weight loss of poeaple one year after using the Atkins diet.How many dieters must be surved if we want to be 95% confident that the sample mean weight loss is within 0.25 lb of the true population mean?Assume that the populatiion standard deviation is known to be 10.6 lb
large sample confidence intervals are used to find a region in which we are 100 (1-α)% confident the true
value of the parameter is in the interval.
For large sample confidence intervals about the mean you have:
xBar ± z * sx / sqrt(n)
where xBar is the sample mean
z is the zscore for having α% of the data in the tails, i.e., P( |Z| > z) = α
sx is the sample standard deviation
n is the sample size
in this question we are only concerned about the error term
z * sx / sqrt(n)
we need to find the value of n such that expression equals 0.25
the z score for the 95% CI is 1.96
solve the equation
z * sx / sqrt(n) = w
n = (z * sx / w) ^ 2
here we have have w = 0.25
n = 6906.275
n must be an integer, always take the ceiling of the calculated value
n = 6907